#### Prof. Dr. Ilya Eremin

Institute for Theoretical Physics, Theoretical Solid State Physics

Ruhr-Universität Bochum

##### Contact

- ilya[dot]eremin[at]rub[dot]de
- +49 0234 32 26604
- personal website

##### Author IDs

- ORCID: 0000-0003-0557-8015
- Scopus: 7005345793
- Google Scholar: lVXJPHMAAAAJ&hl=en&oi=ao

##### Hub

**Electronic correlations and superconducting instability in La3Ni2 O7 under high pressure**

Lechermann, Frank and Gondolf, Jannik and Bötzel, Steffen and Eremin, Ilya M.*Physical Review B*108 (2023)Motivated by the report of superconductivity in bilayer La3Ni2O7 at high pressure, we examine the interacting electrons in this system. First-principles many-body theory is utilized to study the normal-state electronic properties. Below 100 K, a multiorbital non-Fermi-liquid state resulting from a loss of Ni-ligand coherence within a flat-band-dominated low-energy landscape is uncovered. The incoherent low-temperature Fermi surface displays strong mixing between Ni-dz2 and Ni-dx2-y2 orbital character. In a model Hamiltonian picture, spin fluctuations originating mostly from the Ni-dz2 orbital give rise to strong tendencies towards a superconducting instability with a B1g or B2g order parameter. The dramatic enhancement of Tc in pressurized La3Ni2O7 is due to stronger Ni-dz2 correlations compared to those in the infinite-layer nickelates. © 2023 American Physical Society.view abstract 10.1103/PhysRevB.108.L201121 **Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)**

Walker, M. and Scott, K. and Boyle, T.J. and Byland, J.K. and Bötzel, S. and Zhao, Z. and Day, R.P. and Zhdanovich, S. and Gorovikov, S. and Pedersen, T.M. and Klavins, P. and Damascelli, A. and Eremin, I.M. and Gozar, A. and Taufour, V. and da Silva Neto, E.H.*npj Quantum Materials*8 (2023)FeSe1−xS x remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1−xS x with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates. © 2023, Springer Nature Limited.view abstract 10.1038/s41535-023-00592-5 **Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints**

Neyenhuys, Oliver and Fistul, Mikhail V. and Eremin, Ilya M.*Physical Review B*108 (2023)Geometrical frustration in correlated systems can give rise to a plethora of ordered states and intriguing phases. Here, we theoretically analyze vertex-sharing frustrated Kagome lattices of Josephson junctions and identify various classical and quantum phases. The frustration is provided by periodically arranged 0- and π-Josephson junctions. In the frustrated regime, the macroscopic phases are composed of different patterns of vortices/antivortices penetrating each basic element of the Kagome lattice, i.e., a superconducting triangle interrupted by three Josephson junctions. We obtain that numerous topological constraints, related to the flux quantization in any hexagon loop, lead to highly anisotropic and long-range interaction between well separated vortices/antivortices. Considering this interaction and a possibility of macroscopic tunneling between vortex and antivortex in single superconducting triangles, we derive an effective Ising-type spin Hamiltonian with strongly anisotropic long-range interaction. In the classically frustrated regime, we numerically calculate the temperature-dependent spatially averaged spin polarization m¯(T) characterizing the crossover between the ordered and disordered vortex/antivortex states. In the coherent quantum regime, we analyze the lifting of the degeneracy of the ground state and the appearance of the highly entangled states. © 2023 American Physical Society.view abstract 10.1103/PhysRevB.108.165413 **Persistent current-carrying state of charge quasiparticles in an np ribbon featuring a single Dirac cone**

Kadigrobov, Anatoly M. and Eremin, Ilya M.*Physical Review B*108 (2023)The formation of persistent charge currents in mesoscopic systems remains an interesting and actual topic of condensed matter research. Here, we analyze the formation of spontaneous arising persistent currents of charged fermions in two-dimensional electron-hole ribbons on the top and bottom of a three-dimensional topological insulator. In such a device the two-dimensional Dirac fermions with opposite chiralities are spatially separated, which allows these currents to flow in the opposite directions without compensating each other. The nature of this phenomenon is based on the interference of the quasiparticle quantum waves that are scattered with asymmetric scattering phases at the lateral np chiral junction and then reflected back by the external boundaries of the ribbon. As a result, quasiparticles in the ribbon are shown to be in unified electron-hole quantum states carrying the persistent current. © 2023 American Physical Society.view abstract 10.1103/PhysRevB.108.155407 **Quantum phase transitions in non-Hermitian PT-symmetric transverse-field Ising spin chains**

Starkov, Grigory A. and Fistul, Mikhail V. and Eremin, Ilya M.*Annals of Physics*456 (2023)We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian PT-symmetric superconducting qubits chains described by a transverse-field Ising spin model. A non-Hermitian part of the Hamiltonian is implemented via imaginary staggered longitudinal magnetic field, which corresponds to a local staggered gain and loss terms. By making use of a direct numerical diagonalization of the Hamiltonian for spin chains of a finite size N, we explore the dependencies of the energy spectrum, including the energy difference between the first excited and the ground states, the spatial correlation function of local polarization (z-component of local magnetization) on the adjacent spins interaction strength J and the local gain (loss) parameter γ. A scaling procedure for the correlation length ξ allows us to establish a complete quantum phase diagram of the system. We obtain two quantum phases for J<0, namely, PT-symmetry broken antiferromagnetic state and PT-symmetry preserved paramagnetic state, and the quantum phase transition line between them is the line of exception points. For J>0 the PT-symmetry of the ground state is retained in a whole region of parameter space of J and γ, and a system shows two intriguing quantum phase transitions between ferromagnetic and paramagnetic states for a fixed parameter γ>1. We also provide the qualitative quantum phase diagram γ−J derived in the framework of the Bethe–Peierls approximation that is in a good accord with numerically obtained results. © 2023 Elsevier Inc.view abstract 10.1016/j.aop.2023.169268 **Revisiting the metal-to-metal transition in 2H-AgNiO2**

Gondolf, Jannik and Eremin, Ilya M. and Lechermann, Frank*EPL*144 (2023)The layered delafossite compound AgNiO2 with stacking symmetry undergoes a structural metal-to-metal transition at . It has been described in the past as a charge-ordering transition, where local S = 1 spins are formed on part of the Ni sites. By means of first-principles many-body calculations, we show that the transition is in fact a site-selective Mott transition on the Ni sublattice with only minor charge differentiation. Key to this finding is the uncovering of ligand-hole physics, rendering a Ni2+ instead of a formal Ni3+ oxidation state, in conjunction with strong local Coulomb repulsions. Copyright © 2023 The author(s)view abstract 10.1209/0295-5075/ad0d1d **Schrieffer-Wolff transformation for non-Hermitian systems: Application for PT -symmetric circuit QED**

Starkov, Grigory A. and Fistul, Mikhail V. and Eremin, Ilya M.*Physical Review B*108 (2023)Combining non-Hermiticity and interactions yields unique effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation, discuss its symmetry properties, and derive the effective Hamiltonian suitable for various quasidegenerate non-Hermitian systems. We apply our results to an exemplary PT-symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as |ωr-ω| ωr, where ω and ωr are qubits and resonator frequencies, respectively, providing well-defined groups of quasidegenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator g and the gain (loss) parameter γ, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify PT-symmetry broken and unbroken phases, trace the formation of exceptional points of the second and the third order, and provide a complete phase diagram g-γ of low-lying resonant states. We relate the formation of exceptional points to the additional P-pseudo-Hermitian symmetry of the system and show that non-Hermiticity mixes the "dark"and the "bright"states, which has a direct experimental consequence. © 2023 American Physical Society.view abstract 10.1103/PhysRevB.108.235417 **Special issue in memory of Prof. Konstantin B. Efetov: Editorial foreword**

Chubukov, Andrey V. and Eremin, Ilya M. and Galitski, Victor and Pepin, Catherine*Annals of Physics*456 (2023)view abstract 10.1016/j.aop.2023.169366 **Unusual crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superconductivity in iron chalcogenides**

Mizukami, Yuta and Haze, Masahiro and Tanaka, Ohei and Matsuura, Kohei and Sano, Daiki and Böker, Jakob and Eremin, Ilya and Kasahara, Shigeru and Matsuda, Yuji and Shibauchi, Takasada*Communications Physics*6 (2023)The BCS-BEC (Bardeen-Cooper-Schrieffer–Bose-Einstein-condensate) crossover from strongly overlapping Cooper pairs to non-overlapping composite bosons in the strong coupling limit has been a long-standing issue of interacting many-body fermion systems. Recently, FeSe semimetal with hole and electron bands emerged as a high-transition-temperature (high-T c) superconductor located in the BCS-BEC crossover regime, owing to its very small Fermi energies. In FeSe, however, an ordinary BCS-like heat-capacity jump is observed at T c, posing a fundamental question on the characteristics of the BCS-BEC crossover. Here we report on high-resolution heat capacity, magnetic torque, and scanning tunneling spectroscopy measurements in FeSe1−xS x. Upon entering the tetragonal phase at x > 0.17, where nematic order is suppressed, T c discontinuously decreases. In this phase, highly non-mean-field behaviours consistent with BEC-like pairing are found in the thermodynamic quantities with giant superconducting fluctuations extending far above T c, implying the change of pairing nature. Moreover, the pseudogap formation, which is expected in BCS-BEC crossover of single-band superconductors, is not observed in the tunneling spectra. These results illuminate highly unusual features of the superconducting states in the crossover regime with multiband electronic structure and competing electronic instabilities. © 2023, The Author(s).view abstract 10.1038/s42005-023-01289-8 **Charge and spin supercurrents in magnetic Josephson junctions with spin filters and domain walls**

Dahir, S.M. and Volkov, A.F. and Eremin, I.M.*Physical Review B*105 (2022)view abstract 10.1103/PhysRevB.105.094517 **Feedback of Non-Local dxy Nematicity on the Magnetic Anisotropy in FeSe**

Bötzel, S. and Eremin, I.M.*Frontiers in Physics*10 (2022)view abstract 10.3389/fphy.2022.919784 **High-order nonlinear terahertz probing of the two-band superconductor MgB2: Third- and fifth-order harmonic generation**

Reinhoffer, C. and Pilch, P. and Reinold, A. and Derendorf, P. and Kovalev, S. and Deinert, J.-C. and Ilyakov, I. and Ponomaryov, A. and Chen, M. and Xu, T.-Q. and Wang, Y. and Gan, Z.-Z. and Wu, D.-S. and Luo, J.-L. and Germanskiy, S. and Mashkovich, E.A. and Van Loosdrecht, P.H.M. and Eremin, I.M. and Wang, Z.*Physical Review B*106 (2022)view abstract 10.1103/PhysRevB.106.214514 **Linear response for pseudo-Hermitian Hamiltonian systems: Application to PT -symmetric qubits**

Tetling, L. and Fistul, M.V. and Eremin, I.M.*Physical Review B*106 (2022)view abstract 10.1103/PhysRevB.106.134511 **Quantum dynamics of disordered arrays of interacting superconducting qubits: Signatures of quantum collective states**

Fistul, M.V. and Neyenhuys, O. and Bocaz, A.B. and Lisitskiy, M. and Eremin, I.M.*Physical Review B*105 (2022)view abstract 10.1103/PhysRevB.105.104516 **Signatures of collective modes in fifth harmonic generation of BCS superconductor**

Derendorf, P. and Müller, M.A. and Eremin, I.M.*Faraday Discussions*237 (2022)view abstract 10.1039/d2fd00067a **Superconducting Instabilities in Strongly Correlated Infinite-Layer Nickelates**

Kreisel, A. and Andersen, B.M. and Rømer, A.T. and Eremin, I.M. and Lechermann, F.*Physical Review Letters*129 (2022)view abstract 10.1103/PhysRevLett.129.077002 **Ab initio study of the structural response to magnetic disorder and van der Waals interactions in FeSe**

Lochner, F. and Eremin, I.M. and Hickel, T. and Neugebauer, J.*Physical Review B*103 (2021)The electronic structure in unconventional superconductors holds a key to understanding the momentum-dependent pairing interactions and the resulting superconducting gap function. In superconducting Fe-based chalcogenides, there have been controversial results regarding the importance of the kz dependence of the electronic dispersion, the gap structure, and the pairing mechanisms. Here, we use density functional theory to investigate the underlying structural properties in combination with a sophisticated real-space treatment of magnetic disorder for the prototype system FeSe. Our calculations demonstrate that interlayer and intralayer interactions need to be considered and that charge-driven van der Waals interactions between Se atoms instead of magnetic coupling effects drive the interlayer binding. The methodological advances and physical insights are important for upcoming investigations of the three-dimensional effects, including nontrivial topology, of FeSe1-xTex and FeSe1-xSx systems. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.103.054506 **Direct visualization of a static incommensurate antiferromagnetic order in Fe-doped Bi2Sr2CaCu2O8+δ**

Wan, S. and Li, H. and Choubey, P. and Gu, Q. and Li, H. and Yang, H. and Eremin, I.M. and Gu, G. and Wen, H.-H.*Proceedings of the National Academy of Sciences of the United States of America*118 (2021)In cuprate superconductors, due to strong electronic correlations, there are multiple intertwined orders which either coexist or compete with superconductivity. Among them, the antiferromagnetic (AF) order is the most prominent one. In the region where superconductivity sets in, the long-range AF order is destroyed. Yet the residual short-range AF spin fluctuations are present up to a much higher doping, and their role in the emergence of the superconducting phase is still highly debated. Here, by using a spin-polarized scanning tunneling microscope, we directly visualize an emergent incommensurate AF order in the nearby region of Fe impurities embedded in the optimally doped Bi2Sr2CaCu2O8+δ (Bi2212). Remarkably, the Fe impurities suppress the superconducting coherence peaks with the gapped feature intact, but pin down the ubiquitous short-range incommensurate AF order. Our work shows an intimate relation between antiferromagnetism and superconductivity. © 2021 National Academy of Sciences. All rights reserved.view abstract 10.1073/pnas.2115317118 **Electronic theory for scanning tunneling microscopy spectra in infinite-layer nickelate superconductors**

Choubey, P. and Eremin, I.M.*Physical Review B*104 (2021)The recent scanning tunneling microscopy (STM) observation of -shaped and -shaped spectra (and their mixture) in superconducting thin films has been interpreted as the presence of two distinct gap symmetries in this nickelate superconductor [Gu, Nat. Commun.11, 6027 (2020)10.1038/s41467-020-19908-1]. Here, using a two-band model of nickelates capturing dominant contributions from Ni- and rare-earth (R)- orbitals, we show that the experimental observation can be simply explained within a pairing scenario characterized by a conventional -wave gap structure with the lowest harmonic on the Ni band and a -wave gap with higher harmonics on the R band. We perform realistic simulations of STM spectra employing first-principles Wannier functions to properly account for the tunneling processes and obtain and mixed spectral line shapes depending on the position of the STM tip within the unit cell. The - and -shaped spectra are contributed by Ni and R bands, respectively, and Wannier functions, in essence, provide position-dependent weighting factors, determining the spectral line shape at a given intra-unit-cell position. We propose a phase-sensitive experiment to distinguish between the proposed -wave gap structure and the time-reversal symmetry-breaking gap which yields very similar intra-unit-cell spectra. © 2021 American Physical Societyview abstract 10.1103/PhysRevB.104.144504 **Finite temperature fluctuation-induced order and responses in magnetic topological insulators**

Scholten, M. and Facio, J.I. and Ray, R. and Eremin, I.M. and van den Brink, J. and Nogueira, F.S.*Physical Review Research*3 (2021)We derive an effective field theory model for magnetic topological insulators and predict that a magnetic electronic gap persists on the surface for temperatures above the ordering temperature of the bulk. Our analysis also applies to interfaces of heterostructures consisting of a ferromagnetic and a topological insulator. In order to make quantitative predictions for and for EuS- heterostructures, we combine the effective field theory method with density functional theory and Monte Carlo simulations. For we predict an upwards Néel temperature shift at the surface up to , while the EuS- interface exhibits a smaller relative shift. The effective theory also predicts induced Dzyaloshinskii-Moriya interactions and a topological magnetoelectric effect, both of which feature a finite temperature and chemical potential dependence. © 2021 Published by the American Physical Societyview abstract 10.1103/PhysRevResearch.3.L032014 **Interplay between nematicity and Bardasis-Schrieffer modes in the short-time dynamics of unconventional superconductors**

Müller, M.A. and Volkov, P.A. and Paul, I. and Eremin, I.M.*Physical Review B*103 (2021)Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of iron-based and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a nonequilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merges into a single in-gap mode, with the mixing vanishing only close to the phase boundaries. For the d-wave ground state, we find that nematic interaction suppresses the damping of the collective oscillations in the short-time dynamics. Additionally, we find that even inside the nematic s+d-wave superconducting state, a Bardasis-Schrieffer-like mode leads to order parameter oscillations that strongly depend on the competition between the two pairing symmetries. We discuss the connection of our results to the recent pump-probe experiments on high-Tc superconductors. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.103.024519 **Mn-induced Fermi-surface reconstruction in the SmFeAsO parent compound**

Meinero, M. and Bonfà, P. and Onuorah, I.J. and Sanna, S. and De Renzi, R. and Eremin, I. and Müller, M.A. and Orain, J.-C. and Martinelli, A. and Provino, A. and Manfrinetti, P. and Putti, M. and Shiroka, T. and Lamura, G.*Scientific Reports*11 (2021)The electronic ground state of iron-based materials is unusually sensitive to electronic correlations. Among others, its delicate balance is profoundly affected by the insertion of magnetic impurities in the FeAs layers. Here, we address the effects of Fe-to-Mn substitution in the non-superconducting Sm-1111 pnictide parent compound via a comparative study of SmFe1-xMnxAsO samples with x(Mn) = 0.05 and 0.10. Magnetization, Hall effect, and muon-spin spectroscopy data provide a coherent picture, indicating a weakening of the commensurate Fe spin-density-wave (SDW) order, as shown by the lowering of the SDW transition temperature TSDW with increasing Mn content, and the unexpected appearance of another magnetic order, occurring at T∗≈ 10 and 20 K for x= 0.05 and 0.10, respectively. We attribute the new magnetic transition at T∗, occurring well inside the SDW phase, to a reorganization of the Fermi surface due to Fe-to-Mn substitutions. These give rise to enhanced magnetic fluctuations along the incommensurate wavevector Q2= (π± δ, π± δ) , further increased by the RKKY interactions among Mn impurities. © 2021, The Author(s).view abstract 10.1038/s41598-021-93625-7 **Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination**

Sharma, R. and Kreisel, A. and Sulangi, M.A. and Böker, J. and Kostin, A. and Allan, M.P. and Eisaki, H. and Böhmer, A.E. and Canfield, P.C. and Eremin, I. and Séamus Davis, J.C. and Hirschfeld, P.J. and Sprau, P.O.*npj Quantum Materials*6 (2021)Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap Δkα, for all momenta k on the Fermi surface of every band α. While there are a variety of techniques for determining ∣Δkα∣, no general method existed to measure the signed values of Δkα. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where Δkα has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the Δkα it generates to the Δkα determined from single-atom scattering in FeSe where s± energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for Δkα of opposite sign. © 2021, Crown.view abstract 10.1038/s41535-020-00303-4 **Non-local dx y nematicity and the missing electron pocket in FeSe**

Rhodes, L.C. and Böker, J. and Müller, M.A. and Eschrig, M. and Eremin, I.M.*npj Quantum Materials*6 (2021)The origin of spontaneous electronic nematic ordering provides important information for understanding iron-based superconductors. Here, we analyze a scenario where the dxy orbital strongly contributes to nematic ordering in FeSe. We show that the addition of dxy nematicity to a pure dxz/dyz order provides a natural explanation for the unusual Fermi surface and correctly reproduces the strongly anisotropic momentum dependence of the superconducting gap. We predict a Lifshitz transition of an electron pocket mediated by temperature and sulfur doping, whose signatures we discuss by analysing available experimental data. We present the variation of momentum dependence of the superconducting gap upon suppression of nematicity. Our quantitatively accurate model yields the transition from tetragonal to nematic FeSe and the FeSe1−xSx series, and puts strong constraints on possible nematic mechanisms. © 2021, The Author(s).view abstract 10.1038/s41535-021-00341-6 **Signatures of Bardasis-Schrieffer mode excitation in third-harmonic generated currents**

Müller, M.A. and Eremin, I.M.*Physical Review B*104 (2021)We theoretically analyze collective modes in unconventional superconductors focusing on the Bardasis-Schrieffer (BS) mode and its contribution to the third-harmonic generation currents. Starting from a model with competing superconducting pairing instabilities we add fluctuations of the fields beyond the saddle point approximation and calculate their response to a driving electric field. To model phase fluctuations appropriately we take into account the effect of the long-range Coulomb interaction. While the phase mode is pushed into a plasmon frequency, as known from the literature, we show that the BS mode remains unaffected. Furthermore, it has a characteristic polarization dependence and, unlike the Higgs mode, generates a current in the perpendicular direction to the applied field. We find that the Bardasis-Schrieffer excitations contribute a sizable signal to the third-harmonic generated current, which is clearly distinguishable from the charge density fluctuations due to Cooper-pair-breaking effects and can be straightforwardly detected in experiment. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.104.144508 **Specific heat and gap structure of a nematic superconductor: Application to FeSe**

Islam, K.R. and Böker, J. and Eremin, I.M. and Chubukov, A.V.*Physical Review B*104 (2021)We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multiorbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which coexists with nematicity. We analyze the angular dependence of the gap function and specific heat of such a nematic superconductor. We specifically address three issues: (i) the angular dependence of the gap in light of the competition between the nematicity-induced mixture and the orbital transmutation of low-energy excitations in the nematic state, (ii) the effect of nematicity on the magnitude of the jump of the specific heat at and the temperature dependence of below , and (iii) a potential transition at from an state to an state that breaks time-reversal symmetry. We consider two scenarios for a nematic order: scenario A, in which this order develops between and orbitals on hole and electron pockets, and scenario B, in which there is an additional component of the nematic order for fermions on the two electron pockets. ©2021 American Physical Societyview abstract 10.1103/PhysRevB.104.094522 **Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models**

Alcalde Puente, D. and Eremin, I.M.*Physical Review B*102 (2020)Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. Here we employ the convolutional restricted Boltzmann machine (CRBM) method and show that its use helps to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, we show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM we apply it to the paradigmatic Ising and Kitaev models in two dimensions. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.195148 **Detection of squeezed phonons in pump-probe spectroscopy**

Lakehal, M. and Schiró, M. and Eremin, I.M. and Paul, I.*Physical Review B*102 (2020)Robust engineering of phonon squeezed states in optically excited solids has emerged as a promising tool to control and manipulate their properties. However, in contrast to quantum optical systems, detection of phonon squeezing is subtle and elusive, and an important question is what constitutes an unambiguous signature of it. The state of the art involves observing oscillations at twice the phonon frequency in time-resolved measurements of the out-of-equilibrium phonon fluctuation. Using the Keldysh formalism we show that such a signal is a necessary but not a sufficient signature of a squeezed phonon, since we identify several mechanisms that do not involve squeezing and yet produce similar oscillations. We show that reliable detection requires a time- and frequency-resolved measurement of the phonon spectral function. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.174316 **Dictionary learning in Fourier-transform scanning tunneling spectroscopy**

Cheung, S.C. and Shin, J.Y. and Lau, Y. and Chen, Z. and Sun, J. and Zhang, Y. and Müller, M.A. and Eremin, I.M. and Wright, J.N. and Pasupathy, A.N.*Nature Communications*11 (2020)Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. © 2020, The Author(s).view abstract 10.1038/s41467-020-14633-1 **Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe**

Kasahara, S. and Sato, Y. and Licciardello, S. and Čulo, M. and Arsenijević, S. and Ottenbros, T. and Tominaga, T. and Böker, J. and Eremin, I. and Shibauchi, T. and Wosnitza, J. and Hussey, N.E. and Matsuda, Y.*Physical Review Letters*124 (2020)We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field μ0Hc2ab shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ0H∗≈24 T well below μ0Hc2ab, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe. © 2020 American Physical Society.view abstract 10.1103/PhysRevLett.124.107001 **Meissner currents induced by topological magnetic textures in hybrid superconductor/ferromagnet structures**

Dahir, S.M. and Volkov, A.F. and Eremin, I.M.*Physical Review B*102 (2020)Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing nontrivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray fields, which are therefore essential for the study of these systems. Here, we determine the effective stray field Hstr and the Meissner currents jS in a superconductor/ferromagnet/superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures M(r) in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and Néel-type Sk and also analyze in detail the periodic structures of different types of DW's, that is, Bloch-type DW (BDW) and Néel-type DW (NDW) of finite width with in- and out-of-plane magnetization vector M(x). The spatial dependence of the fields Hstr(r) and Meissner currents jS(r) are shown to be qualitatively different for the case of Bloch- and Néel-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of Néel-type magnetic textures. The depairing factor, which determines the critical temperature Tc and which is related to the vector potential of the stray field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's, the maximum is located at a finite distance within the Sk radius rSk. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for Néel-type structures, the critical temperature Tc in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.014503 **Phase-sensitive determination of nodal d-wave order parameter in single-band and multiband superconductors**

Böker, J. and Sulangi, M.A. and Akbari, A. and Davis, J.C.S. and Hirschfeld, P.J. and Eremin, I.M.*Physical Review B*101 (2020)Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently, a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal d-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized correction to the tunneling density of states due to nonmagnetic impurities in the Born limit and at intermediate-scattering strength shows characteristic features for sign-changing and sign-preserving scattering wave vectors, as well as for the momentum-integrated quantity. Furthermore, using a realistic approach accounting for the Wannier orbitals, we model scanning tunneling microscopy data of Bi2Sr2CaCu2O8+δ, which should allow the comparison of our theory with experimental data. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.101.214505 **Superconductivity with broken time-reversal symmetry inside a superconducting s-wave state**

Grinenko, V. and Sarkar, R. and Kihou, K. and Lee, C.H. and Morozov, I. and Aswartham, S. and Büchner, B. and Chekhonin, P. and Skrotzki, W. and Nenkov, K. and Hühne, R. and Nielsch, K. and Drechsler, S.-L. and Vadimov, V.L. and Silaev, M.A. and Volkov, P.A. and Eremin, I. and Luetkens, H. and Klauss, H.-H.*Nature Physics*16 (2020)In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors in which superconductivity coexists with magnetism, and a few examples are known where the superconductivity itself induces spontaneous magnetism. The best known of these compounds are Sr2RuO4 and some non-centrosymmetric superconductors. Here, we report the finding of a narrow dome of an s+ is′ superconducting phase with apparent broken time-reversal symmetry (BTRS) inside the broad s-wave superconducting region of the centrosymmetric multiband superconductor Ba1 − xKxFe2As2 (0.7 ≲ x ≲ 0.85). We observe spontaneous magnetic fields inside this dome using the muon spin relaxation (μSR) technique. Furthermore, our detailed specific heat study reveals that the BTRS dome appears very close to a change in the topology of the Fermi surface. With this, we experimentally demonstrate the likely emergence of a novel quantum state due to topological changes of the electronic system. © 2020, The Author(s), under exclusive licence to Springer Nature Limited.view abstract 10.1038/s41567-020-0886-9 **Theory of strain-induced magnetic order and splitting of Tc and TTRSB in Sr2Ru O4**

Rømer, A.T. and Kreisel, A. and Müller, M.A. and Hirschfeld, P.J. and Eremin, I.M. and Andersen, B.M.*Physical Review B*102 (2020)The internal structure of the superconducting state in Sr2RuO4 remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature Tc and the onset of time-reversal symmetry breaking TTRSB with applied strain (Grinenko et al., arXiv:2001.08152). In addition, static magnetic order is induced by the uniaxial strain beyond ∼1 GPa, indicating that unstrained Sr2RuO4 is close to a magnetic quantum critical point. Here we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. It is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain dependence of accidentally degenerate pair states in unstrained Sr2RuO4. In addition, while unstrained Sr2RuO4 features mainly (2π/3,2π/3) magnetic fluctuations, uniaxial strain promotes (π,±π/2) magnetic order. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.054506 **Collective modes in pumped unconventional superconductors with competing ground states**

Müller, M.A. and Volkov, P.A. and Paul, I. and Eremin, I.M.*Physical Review B*100 (2019)Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band square lattice model with a spin-spin interaction as an example, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse can be used to control the symmetry of the nonequilibrium state as well as frequencies and relative intensities of the contributions of different collective modes. We find particularly strong signatures of the Bardasis-Schrieffer mode in the dynamics of the quasiparticle distribution function. Our work shows the potential of modern ultrafast experiments to address the collective excitations in unconventional superconductors and highlights the importance of subdominant interactions for the nonequilibrium dynamics in these systems. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.100.140501 **Interaction of Skyrmions and Pearl Vortices in Superconductor-Chiral Ferromagnet Heterostructures**

Dahir, S.M. and Volkov, A.F. and Eremin, I.M.*Physical Review Letters*122 (2019)We investigate a hybrid heterostructure with magnetic skyrmions (Sk) inside a chiral ferromagnet interfaced by a thin superconducting film via an insulating barrier. The barrier prevents electronic transport between the superconductor and the chiral magnet, such that the coupling can occur only through the magnetic fields generated by these materials. We find that Pearl vortices (PV) are generated spontaneously in the superconductor within the skyrmion radius, while anti-Pearl vortices (PV) compensating the magnetic moment of the Pearl vortices are generated outside of the Sk radius, forming an energetically stable topological hybrid structure. Finally, we analyze the interplay of skyrmion and vortex lattices and their mutual feedback on each other. In particular, we argue that the size of the skyrmions will be greatly affected by the presence of the vortices, offering another prospect of manipulating the skyrmionic size by the proximity to a superconductor. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.122.097001 **Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr2RuO4**

Rømer, A.T. and Scherer, D.D. and Eremin, I.M. and Hirschfeld, P.J. and Andersen, B.M.*Physical Review Letters*123 (2019)Recent nuclear magnetic resonance studies [A. Pustogow et al., Nature 574, 72 (2019)] have challenged the prevalent chiral triplet pairing scenario proposed for Sr2RuO4. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the γ band to the van Hove points. A surprising near degeneracy of the nodal s′ and dx2-y2 wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken s′+idx2-y2 pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.123.247001 **Phase-dependent spin polarization of Cooper pairs in magnetic Josephson junctions**

Dahir, S.M. and Volkov, A.F. and Eremin, I.M.*Physical Review B*100 (2019)Superconductor-ferromagnet hybrid structures (SF) have attracted much interest in the past decades, due to a variety of interesting phenomena predicted and observed in these structures. One of them is the so-called inverse proximity effect. It is described by a spin polarization of Cooper pairs, which occurs not only in the ferromagnet (F), but also in the superconductor (S), yielding a finite magnetic moment MS inside the superconductor. This effect has been predicted and experimentally studied. However, interpretation of the experimental data is mostly ambiguous. Here, we study theoretically the impact of the spin polarized Cooper pairs on the Josephson effect in an SFS junction. We show that the induced magnetic moment MS does depend on the phase difference φ and, therefore, will oscillate in time with the Josephson frequency 2eV/â., if the current exceeds a critical value. Most importantly, the spin polarization in the superconductor causes a significant change in the Fraunhofer pattern, which can be easily accessed experimentally. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.100.134513 **Quantum Vortex Core and Missing Pseudogap in the Multiband BCS-BEC Crossover Superconductor FeSe**

Hanaguri, T. and Kasahara, S. and Böker, J. and Eremin, I. and Shibauchi, T. and Matsuda, Y.*Physical Review Letters*122 (2019)FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein condensation crossover regime where the superconducting gap size and the superconducting transition temperature Tc are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above Tc may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was not detected. These apparently conflicting observations may be related to the multiband nature of FeSe. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.122.077001 **Quasiparticle interference and symmetry of superconducting order parameter in strongly electron-doped iron-based superconductors**

Böker, J. and Volkov, P.A. and Hirschfeld, P.J. and Eremin, I.*New Journal of Physics*21 (2019)Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li1-xFex(OHFe)1-yZnySe superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states-s-wave, d-wave and helical p-wave-can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intra- A nd inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity A 1g (s-wave) and B 2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/ab2a82 **Detecting sign-changing superconducting gap in LiFeAs using quasiparticle interference**

Altenfeld, D. and Hirschfeld, P.J. and Mazin, I.I. and Eremin, I.*Physical Review B*97 (2018)Using a realistic ten-orbital tight-binding model Hamiltonian fitted to the angle-resolved photoemission spectroscopy data on LiFeAs, we analyze the temperature, frequency, and momentum dependencies of quasiparticle interference to identify gap sign changes in a qualitative way, following our original proposal [Phys. Rev. B 92, 184513 (2015)PRBMDO1098-012110.1103/PhysRevB.92.184513]. We show that all features present for the simple two-band model for the sign-changing s+ - wave superconducting gap employed previously are still present in the realistic tight-binding approximation and gap values observed experimentally. We discuss various superconducting gap structures proposed for LiFeAs and identify various features of these superconducting gap functions in the quasiparticle interference patterns. On the other hand, we show that it will be difficult to identify the more complicated possible sign structures of the hole pocket gaps in LiFeAs due to the smallness of the pockets and the near proximity of two of the gap energies. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.054519 **Fluctuation-induced Néel and Bloch skyrmions at topological insulator surfaces**

Nogueira, F.S. and Eremin, I. and Katmis, F. and Moodera, J.S. and Van Den Brink, J. and Kravchuk, V.P.*Physical Review B*98 (2018)Ferromagnets in contact with a topological insulator have become appealing candidates for spintronics due to the presence of Dirac surface states with spin-momentum locking. Because of this, bilayer Bi2Se3-EuS structures, for instance, show a finite magnetization at the interface at temperatures well exceeding the Curie temperature of bulk EuS. Here, we determine theoretically the effective magnetic interactions at a topological insulator-ferromagnet interface above the magnetic ordering temperature. We show that by integrating out the Dirac fermion fluctuations an effective Dzyaloshinskii-Moriya interaction and magnetic charging interaction emerge. As a result, individual magnetic skyrmions and extended skyrmion lattices can form at the interfaces of ferromagnets and topological insulators, the first indications of which have been very recently observed experimentally. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.060401 **In-plane magnetic penetration depth of superconducting CaKFe4As4**

Khasanov, R. and Meier, W.R. and Wu, Y. and Mou, D. and Bud'Ko, S.L. and Eremin, I. and Luetkens, H. and Kaminski, A. and Canfield, P.C. and Amato, A.*Physical Review B*97 (2018)The temperature dependence of the in-plane magnetic penetration depth (λab) in an extensively characterized sample of superconducting CaKFe4As4(Tc≃35K) was investigated using muon-spin rotation (μSR). A comparison of λab-2(T) measured by μSR with the one inferred from angle-resolved photoemission spectroscopy (ARPES) data confirms the presence of multiple gaps at the Fermi level. An agreement between μSR and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small superconducting gaps with an average zero-temperature value of Δ0=2.4(2)meV. Our data suggest that in CaKFe4As4 the s± order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.140503 **Pressure effects on the electronic properties of the undoped superconductor ThFeAsN**

Barbero, N. and Holenstein, S. and Shang, T. and Shermadini, Z. and Lochner, F. and Eremin, I. and Wang, C. and Cao, G.-H. and Khasanov, R. and Ott, H.-R. and Mesot, J. and Shiroka, T.*Physical Review B*97 (2018)The recently synthesized ThFeAsN iron pnictide superconductor exhibits a Tc of 30 K, the highest of the 1111-type series in the absence of chemical doping. To understand how pressure affects its electronic properties, we carried out microscopic investigations up to 3 GPa via magnetization, nuclear magnetic resonance, and muon-spin rotation experiments. The temperature dependence of the As75 Knight shift, the spin-lattice relaxation rates, and the magnetic penetration depth suggest a multiband s±-wave gap symmetry in the dirty limit, whereas the gap-to-Tc ratio Δ/kBTc hints at a strong-coupling scenario. Pressure modulates the geometrical parameters, thus reducing Tc as well as Tm, the temperature where magnetic-relaxation rates are maximized, both at the same rate of approximately -1.1K/GPa. This decrease in Tc with pressure is consistent with band-structure calculations, which relate it to the deformation of the Fe 3dz2 orbitals. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.140506 **Short-time dynamics in s+is -wave superconductor with incipient bands**

Müller, M.A. and Shen, P. and Dzero, M. and Eremin, I.*Physical Review B*98 (2018)Motivated by the recent observation of the time-reversal symmetry broken state in K-doped BaFe2As2 superconducting alloys, we theoretically study the collective modes and the short time dynamics of the superconducting state with s+is-wave order parameter using an effective four-band model with two hole and two electron pockets. The superconducting s+is state emerges for incipient electron bands as a result of hole doping and appears as an intermediate state between s± (high number of holes) and s++ (low number of holes). The amplitude and phase modes are coupled giving rise to a variety of collective modes. In the s± state, we find that the collective excitations are the Higgs (amplitude) modes, while the Leggett mode is absent due to strong interband interaction. In the s+is and s++ state, we uncover a new coupled collective soft mode. Finally we compare our results with the s+id solution and find similar behavior of the collective modes as in the s+is state. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.024522 **Sign reversal of the order parameter in (Li1-x Fex)OHFe1-y Zny Se**

Du, Z. and Yang, X. and Altenfeld, D. and Gu, Q. and Yang, H. and Eremin, I. and Hirschfeld, P.J. and Mazin, I.I. and Lin, H. and Zhu, X. and Wen, H.-H.*Nature Physics*14 (2018)Iron pnictides are the only known family of unconventional high-temperature superconductors besides cuprates. Until recently, it was widely accepted that superconductivity is driven by spin fluctuations and intimately related to the fermiology, specifically, hole and electron pockets separated by the same wavevector that characterizes the dominant spin fluctuations, and supporting order parameters (OP) of opposite signs. This picture was questioned after the discovery of intercalated or monolayer form of FeSe-based systems without hole pockets, which seemingly undermines the basis for spin-fluctuation theory and the idea of a sign-changing OP. Using the recently proposed phase-sensitive quasiparticle interference technique, here we show that in LiOH-intercalated FeSe compound the OP does change sign, albeit within the electronic pockets. This result unifies the pairing mechanism of iron-based superconductors with or without the hole Fermi pockets and supports the conclusion that spin fluctuations play the key role in electron pairing. © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.view abstract 10.1038/nphys4299 **Spin-orbit coupling, minimal model and potential Cooper-pairing from repulsion in BiS2-superconductors**

Cobo-Lopez, S. and Bahramy, M.S. and Arita, R. and Akbari, A. and Eremin, I.*New Journal of Physics*20 (2018)We develop the realistic minimal electronic model for recently discovered BiS2 superconductors including the spin-orbit (SO) coupling based on the first-principles band structure calculations. Due to strong SO coupling, characteristic for the Bi-based systems, the tight-binding low-energy model necessarily includes p x, p y, and p z orbitals. We analyze a potential Cooper-pairing instability from purely repulsive interaction for the moderate electronic correlations using the so-called leading angular harmonics approximation. For small and intermediate doping concentrations we find the dominant instabilities to be -wave, and s ±-wave symmetries, respectively. At the same time, in the absence of the sizable spin fluctuations the intra and interband Coulomb repulsions are of the same strength, which yield the strongly anisotropic behavior of the superconducting gaps on the Fermi surface. This agrees with recent angle resolved photoemission spectroscopy findings. In addition, we find that the Fermi surface topology for BiS2 layered systems at large electron doping can resemble the doped iron-based pnictide superconductors with electron and hole Fermi surfaces maintaining sufficient nesting between them. This could provide further boost to increase T c in these systems. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aaaf87 **Dichotomy between in-plane magnetic susceptibility and resistivity anisotropies in extremely strained BaFe2As2**

He, M. and Wang, L. and Ahn, F. and Hardy, F. and Wolf, T. and Adelmann, P. and Schmalian, J. and Eremin, I. and Meingast, C.*Nature Communications*8 (2017)High-temperature superconductivity in the Fe-based materials emerges when the antiferromagnetism of the parent compounds is suppressed by either doping or pressure. Closely connected to the antiferromagnetic state are entangled orbital, lattice, and nematic degrees of freedom, and one of the major goals in this field has been to determine the hierarchy of these interactions. Here we present the direct measurements and the calculations of the in-plane uniform magnetic susceptibility anisotropy of BaFe2As2, which help in determining the above hierarchy. The magnetization measurements are made possible by utilizing a simple method for applying a large symmetry-breaking strain, based on differential thermal expansion. In strong contrast to the large resistivity anisotropy above the antiferromagnetic transition at T N, the anisotropy of the in-plane magnetic susceptibility develops largely below T N. Our results imply that lattice and orbital degrees of freedom play a subdominant role in these materials. © 2017 The Author(s).view abstract 10.1038/s41467-017-00712-3 **Electronic properties, low-energy Hamiltonian, and superconducting instabilities in CaKFe4As4**

Lochner, F. and Ahn, F. and Hickel, T. and Eremin, I.*Physical Review B*96 (2017)We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe4As4 by combining an ab initio approach and a projection of the band structure to a low-energy tight-binding Hamiltonian, based on the maximally localized Wannier orbitals of the 3d Fe states. We identify the key symmetries as well as differences and similarities in the electronic structure between CaKFe4As4 and the parent systems CaFe2As2 and KFe2As2. In particular, we find CaKFe4As4 to have a significantly more quasi-two-dimensional electronic structure than the latter systems. Finally, we study the superconducting instabilities in CaKFe4As4 by employing the leading angular harmonics approximation and find two potential A1g-symmetry representations of the superconducting gap to be the dominant instabilities in this system. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.094521 **High-Tc superconductivity in undoped ThFeAsN**

Shiroka, T. and Shang, T. and Wang, C. and Cao, G.-H. and Eremin, I. and Ott, H.-R. and Mesot, J.*Nature Communications*8 (2017)Unlike the widely studied ReFeAsO series, the newly discovered iron-based superconductor ThFeAsN exhibits a remarkably high critical temperature of 30 K, without chemical doping or external pressure. Here we investigate in detail its magnetic and superconducting properties via muon-spin rotation/relaxation and nuclear magnetic resonance techniques and show that ThFeAsN exhibits strong magnetic fluctuations, suppressed below ∼35 K, but no magnetic order. This contrasts strongly with the ReFeAsO series, where stoichiometric parent materials order antiferromagnetically and superconductivity appears only upon doping. The ThFeAsN case indicates that Fermi-surface modifications due to structural distortions and correlation effects are as important as doping in inducing superconductivity. The direct competition between antiferromagnetism and superconductivity, which in ThFeAsN (as in LiFeAs) occurs at already zero doping, may indicate a significant deviation of the s-wave superconducting gap in this compound from the standard s± scenario. © 2017 The Author(s).view abstract 10.1038/s41467-017-00185-4 **S+is superconductivity with incipient bands: Doping dependence and STM signatures**

Böker, J. and Volkov, P.A. and Efetov, K.B. and Eremin, I.*Physical Review B*96 (2017)Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyze the doping evolution of superconductivity in a four-band model across the Lifshitz transition including BCS-BEC crossover effects on the shallow bands. Similar to the BCS case, we find that with hole doping the phase difference between superconducting order parameters of the hole bands change from 0 to π through an intermediate s+is state, breaking time-reversal symmetry (TRS). The transition, however, occurs in the region where electron bands are incipient and chemical potential renormalization in the superconducting state leads to a significant broadening of the s+is region. We further present the qualitative features of the s+is state that can be observed in scanning tunneling microscopy (STM) experiments, also taking incipient bands into account. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.014517 **Scanning tunnelling spectroscopy as a probe of multi-Q magnetic states of itinerant magnets**

Gastiasoro, M.N. and Eremin, I. and Fernandes, R.M. and Andersen, B.M.*Nature Communications*8 (2017)The combination of electronic correlations and Fermi surfaces with multiple nesting vectors can lead to the appearance of complex multi-Q magnetic ground states, hosting unusual states such as chiral density waves and quantum Hall insulators. Distinguishing single-Q and multi-Q magnetic phases is however a notoriously difficult experimental problem. Here we propose theoretically that the local density of states (LDOS) near a magnetic impurity, whose orientation may be controlled by an external magnetic field, can be used to map out the detailed magnetic configuration of an itinerant system and distinguish unambiguously between single-Q and multi-Q phases. We demonstrate this concept by computing and contrasting the LDOS near a magnetic impurity embedded in three different magnetic ground states relevant to iron-based superconductors - one single-Q and two double-Q phases. Our results open a promising avenue to investigate the complex magnetic configurations in itinerant systems via standard scanning tunnelling spectroscopy, without requiring spin-resolved capability. © The Author(s) 2017.view abstract 10.1038/ncomms14317 **Surface State Tunneling Signatures in the Two-Component Superconductor UPt3**

Lambert, F. and Akbari, A. and Thalmeier, P. and Eremin, I.*Physical Review Letters*118 (2017)Quasiparticle interference (QPI) imaging of Bogoliubov excitations in quasi-two-dimensional unconventional superconductors has become a powerful technique for measuring the superconducting gap and its symmetry. Here, we present the extension of this method to three-dimensional superconductors and analyze the expected QPI spectrum for the two-component heavy-fermion superconductor UPt3 whose gap structure is still controversial. Starting from a 3D electronic structure and the three proposed chiral gap models E1g,u or E2u, we perform a slab calculation that simultaneously gives extended bulk states and topologically protected in-gap dispersionless surface states. We show that the number of Weyl arcs and their hybridization with the line node provides a fingerprint that may finally determine the true nodal structure of the UPt3 superconductor. © 2017 American Physical Society.view abstract 10.1103/PhysRevLett.118.087004 **A higherature ferromagnetic topological insulating phase by proximity coupling**

Katmis, F. and Lauter, V. and Nogueira, F.S. and Assaf, B.A. and Jamer, M.E. and Wei, P. and Satpati, B. and Freeland, J.W. and Eremin, I. and Heiman, D. and Jarillo-Herrero, P. and Moodera, J.S.*Nature*533 (2016)Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices. Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena. In particular, achieving robust long-range magnetic order at the surface of the topological insulator at specific locations without introducing spin-scattering centres could open up new possibilities for devices. Here we use spin-polarized neutron reflectivity experiments to demonstrate topologically enhanced interface magnetism by coupling a ferromagnetic insulator (EuS) to a topological insulator (Bi2Se3) in a bilayer system. This interfacial ferromagnetism persists up to room temperature, even though the ferromagnetic insulator is known to order ferromagnetically only at low temperatures (17 K). The magnetism induced at the interface resulting from the large spin-orbit interaction and the spin-momentum locking of the topological insulator surface greatly enhances the magnetic ordering (Curie) temperature of this bilayer system. The ferromagnetism extends ∼2 nm into the Bi2Se3 from the interface. Owing to the short-range nature of the ferromagnetic exchange interaction, the time-reversal symmetry is broken only near the surface of a topological insulator, while leaving its bulk states unaffected. The topological magneto-electric response originating in such an engineered topological insulator could allow efficient manipulation of the magnetization dynamics by an electric field, providing an energy-efficient topological control mechanism for future spin-based technologies. © 2016 Macmillan Publishers Limited.view abstract 10.1038/nature17635 **Anisotropic spin fluctuations in Sr2RuO4: Role of spin-orbit coupling and induced strain**

Cobo, S. and Ahn, F. and Eremin, I. and Akbari, A.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)We analyze the spin anisotropy of the magnetic susceptibility of Sr2RuO4 in the presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the angle-resolved photoemission spectroscopy results. Similar to the previous observations we find the in-plane polarization of the low-q magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave-vector Q1=(2/3π,2/3π) but also nearly isotropic fluctuations near Q2=(π/6,π/6). Furthermore, one finds that, apart from the high-symmetry direction of the tetragonal Brillouin zone, the magnetic anisotropy is maximal, i.e., χxx≠χyy≠χzz reflected in the x polarization of the intraband nesting wave-vector Q3=(π/2,π). This is a consequence of the orbital anisotropy of the t2g orbitals in momentum space. We also study how the magnetic anisotropy evolves in the presence of the strain and find strong Ising-like ferromagnetic fluctuations near the Lifshitz transition for the xy band. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.224507 **Collective magnetic excitations of C4 -symmetric magnetic states in iron-based superconductors**

Scherer, D.D. and Eremin, I. and Andersen, B.M.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)We study the collective magnetic excitations of the recently discovered C4-symmetric spin-density-wave states of iron-based superconductors with particular emphasis on their orbital character based on an itinerant multiorbital approach. This is important since the C4-symmetric spin-density-wave states exist only at moderate interaction strengths where damping effects from a coupling to the continuum of particle-hole excitations strongly modify the shape of the excitation spectra compared to predictions based on a local moment picture. We uncover a distinct orbital polarization inherent to magnetic excitations in C4-symmetric states, which provide a route to identify the different commensurate magnetic states appearing in the continuously updated phase diagram of the iron-pnictide family. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.180405 **Double-Q spin-density wave in iron arsenide superconductors**

Allred, J.M. and Taddei, K.M. and Bugaris, D.E. and Krogstad, M.J. and Lapidus, S.H. and Chung, D.Y. and Claus, H. and Kanatzidis, M.G. and Brown, D.E. and Kang, J. and Fernandes, R.M. and Eremin, I. and Rosenkranz, S. and Chmaissem, O. and Osborn, R.*Nature Physics*12 (2016)Elucidating the nature of the magnetic ground state of iron-based superconductors is of paramount importance in unveiling the mechanism behind their high-temperature superconductivity. Until recently, it was thought that superconductivity emerges only from an orthorhombic antiferromagnetic stripe phase, which can in principle be described in terms of either localized or itinerant spins. However, we recently reported that tetragonal symmetry is restored inside the magnetically ordered state of certain hole-doped compounds, revealing the existence of a new magnetic phase at compositions close to the onset of superconductivity. Here, we present Mössbauer data that show that half of the iron sites in this tetragonal phase are non-magnetic, establishing conclusively the existence of a novel magnetic ground state with a non-uniform magnetization that is inconsistent with localized spins. Instead, this state is naturally explained as the interference between two commensurate spin-density waves, a rare example of collinear double-Q magnetic order. Our results demonstrate the itinerant character of the magnetism of the iron pnictides, and the primary role played by magnetic degrees of freedom in determining their phase diagram. © 2016 Macmillan Publishers Limited.view abstract 10.1038/nphys3629 **Enhancement of the Superconducting Gap by Nesting in CaKFe4As4: A New High Temperature Superconductor**

Mou, D. and Kong, T. and Meier, W.R. and Lochner, F. and Wang, L.-L. and Lin, Q. and Wu, Y. and Bud'Ko, S.L. and Eremin, I. and Johnson, D.D. and Canfield, P.C. and Kaminski, A.*Physical Review Letters*117 (2016)We use high resolution angle resolved photoemission spectroscopy and density functional theory with measured crystal structure parameters to study the electronic properties of CaKFe4As4. In contrast to the related CaFe2As2 compounds, CaKFe4As4 has a high Tc of 35 K at stochiometric composition. This presents a unique opportunity to study the properties of high temperature superconductivity in the iron arsenides in the absence of doping or substitution. The Fermi surface consists of several hole and electron pockets that have a range of diameters. We find that the values of the superconducting gap are nearly isotropic (within the explored portions of the Brillouin zone), but are significantly different for each of the Fermi surface (FS) sheets. Most importantly, we find that the momentum dependence of the gap magnitude plotted across the entire Brillouin zone displays a strong deviation from the simple cos(kx)cos(ky) functional form of the gap function, proposed by the scenario of Cooper pairing driven by a short range antiferromagnetic exchange interaction. Instead, the maximum value of the gap is observed on FS sheets that are closest to the ideal nesting condition, in contrast to previous observations in other ferropnictides. These results provide strong support for the multiband character of superconductivity in CaKFe4As4, in which Cooper pairing forms on the electron and the hole bands interacting via a dominant interband repulsive interaction, enhanced by band nesting. © 2016 American Physical Society.view abstract 10.1103/PhysRevLett.117.277001 **Investigation of magnetic phases in parent compounds of iron-chalcogenides via quasiparticle scattering interference**

Kamble, B. and Akbari, A. and Eremin, I.*EPL*114 (2016)We employ a five-orbital tight-binding model to develop the mean-field solution for various possible spin density wave states in the iron-chalcogenides. The quasiparticle interference (QPI) technique is applied to detect signatures of these states due to scatterings arising from non-magnetic impurities. Apart from the experimentally observed double-striped structure with ordering vector , the QPI method is investigated for the extended-stripe as well as the orthogonal double-stripe phase. We discuss QPI as a possible tool to detect and classify various magnetic structures with different electronic structure reconstruction within the framework of the compound. © CopyrightEPLA, 2016.view abstract 10.1209/0295-5075/114/17001 **Quasiparticle interference from different impurities on the surface of pyrochlore iridates: Signatures of the Weyl phase**

Lambert, F. and Schnyder, A.P. and Moessner, R. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)Weyl semimetals are gapless three-dimensional topological materials where two bands touch at an even number of points in the bulk Brillouin zone. These semimetals exhibit topologically protected surface Fermi arcs, which pairwise connect the projected bulk band touchings in the surface Brillouin zone. Here, we analyze the quasiparticle interference patterns of the Weyl phase when time-reversal symmetry is explicitly broken. We use a multiband d-electron Hubbard Hamiltonian on a pyrochlore lattice, relevant for the pyrochlore iridate R2Ir2O7 (where R is a rare earth). Using exact diagonalization, we compute the surface spectrum and quasiparticle interference (QPI) patterns for various surface terminations and impurities. We show that the spin and orbital texture of the surface states can be inferred from the absence of certain backscattering processes and from the symmetries of the QPI features for nonmagnetic and magnetic impurities. Furthermore, we show that the QPI patterns of the Weyl phase in pyrochlore iridates may exhibit additional interesting features that go beyond those found previously in TaAs. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.165146 **Superconducting phase diagram of itinerant antiferromagnets**

Rømer, A.T. and Eremin, I. and Hirschfeld, P.J. and Andersen, B.M.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)We study the phase diagram of the Hubbard model in the weak-coupling limit for coexisting spin-density-wave order and spin-fluctuation-mediated superconductivity. Both longitudinal and transverse spin fluctuations contribute significantly to the effective interaction potential, which creates Cooper pairs of the quasiparticles of the antiferromagnetic metallic state. We find a dominant dx2-y2-wave solution in both electron- and hole-doped cases. In the quasi-spin-triplet channel, the longitudinal fluctuations give rise to an effective attraction supporting a p-wave gap, but are overcome by repulsive contributions from the transverse fluctuations which disfavor p-wave pairing compared to dx2-y2. The subleading pair instability is found to be in the g-wave channel, but complex admixtures of d and g are not energetically favored since their nodal structures coincide. Inclusion of interband pairing, in which each fermion in the Cooper pair belongs to a different spin-density-wave band, is considered for a range of electron dopings in the regime of well-developed magnetic order. We demonstrate that these interband pairing gaps, which are nonzero in the magnetic state, must have the same parity under inversion as the normal intraband gaps. The self-consistent solution to the full system of five coupled gap equations gives intraband and interband pairing gaps of dx2-y2 structure and similar gap magnitude. In conclusion, the dx2-y2 gap dominates for both hole and electron doping inside the spin-density-wave phase. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.174519 **Superconductivity versus bound-state formation in a two-band superconductor with small Fermi energy: Applications to Fe pnictides/chalcogenides and doped SrTiO3**

Chubukov, A.V. and Eremin, I. and Efremov, D.V.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in a 2D model of interacting fermions with small Fermi energy EF and weak attractive interaction, which extends to energies well above EF. The 2D case is special because a two-particle bound state forms at arbitrary weak interaction, and already at weak coupling, one has to distinguish between the bound-state formation and superconductivity. We briefly review the situation in the one-band model and then consider two different two-band models: one with one hole band and one electron band and another with two hole or two electron bands. In each case, we obtain the bound-state energy 2E0 for two fermions in a vacuum and solve the set of coupled equations for the pairing gaps and the chemical potentials to obtain the onset temperature of the pairing Tins and the quasiparticle dispersion at T=0. We then compute the superfluid stiffness ρs(T=0) and obtain the actual Tc. For definiteness, we set EF in one band to be near zero and consider different ratios of E0 and EF in the other band. We show that at EF-E0, the behavior of both two-band models is BCS-like in the sense that Tc≈Tins EF and Δ∼Tc. At EF-E0, the two models behave differently: in the model with two hole/two electron bands, Tins∼E0/lnE0EF, Δ∼(E0EF)1/2, and Tc∼EF, like in the one-band model. In between Tins and Tc, the system displays a preformed pair behavior. In the model with one hole and one electron bands, Tc remains of order Tins, and both remain finite at EF=0 and of the order of E0. The preformed pair behavior still does exist in this model because Tc is numerically smaller than Tins. For both models, we reexpress Tins in terms of the fully renormalized two-particle scattering amplitude by extending to the two-band case (the method pioneered by Gorkov and Melik-Barkhudarov back in 1961). We apply our results for the model with a hole and an electron band to Fe pnictides and Fe chalcogenides in which a superconducting gap has been detected on the bands that do not cross the Fermi level, and to FeSe, in which the superconducting gap is comparable to the Fermi energy. We apply the results for the model with two electron bands to Nb-doped SrTiO3 and argue that our theory explains the rapid increase of Tc when both bands start crossing the Fermi level. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.174516 **Doping asymmetry of superconductivity coexisting with antiferromagnetism in spin fluctuation theory**

Rowe, W. and Eremin, I. and Rømer, A.T. and Andersen, B.M. and Hirschfeld, P.J.*New Journal of Physics*17 (2015)We generalize the theory of Cooper-pairing by spin excitations in the metallic antiferromagnetic state to include situations with electron and/or hole pockets. We show that Cooper-pairing arises from transverse spin waves and from gapped longitudinal spin fluctuations of comparable strength. However, each of these interactions, projected on a particular symmetry of the superconducting gap, acts primarily within one type of pocket. We find a nodeless -wave state is supported primarily by the longitudinal fluctuations on the electron pockets, and both transverse and longitudinal fluctuations support nodal -wave symmetry on the hole pockets. Our results may be relevant to the asymmetry of the AF/SC coexistence state in the cuprate phase diagram. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/17/2/023022 **Higgs mechanism, phase transitions, and anomalous Hall effect in three-dimensional topological superconductors**

Nogueira, F.S. and Sudbø, A. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axionlike magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically nontrivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically nontrivial one. One consequence of our analysis of quantum critical fluctuations is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low-frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of but quite distinct in physical origin from the anomalous Hall effect observed in high-Tc superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is nondissipative and occurs in the absence of vortices. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.224507 **Mutual Independence of Critical Temperature and Superfluid Density under Pressure in Optimally Electron-Doped Superconducting LaFeAsO1-xFx**

Prando, G. and Hartmann, Th. and Schottenhamel, W. and Guguchia, Z. and Sanna, S. and Ahn, F. and Nekrasov, I. and Blum, C.G.F. and Wolter, A.U.B. and Wurmehl, S. and Khasanov, R. and Eremin, I. and Büchner, B.*Physical Review Letters*114 (2015)The superconducting properties of LaFeAsO1-xFx under conditions of optimal electron doping are investigated upon the application of external pressure up to ∼ 23 kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a clear mutual independence between the critical temperature Tc and the low-temperature saturation value for the ratio ns/m∗ (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of ∼ 30% is reported for ns/m∗ at the maximum pressure value while Tc is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of nonmagnetic impurities on multiband superconductivity into account. In particular, the unique possibility to modify the ratio between intraband and interband scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model. © 2015 American Physical Society.view abstract 10.1103/PhysRevLett.114.247004 **Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: A numerical RPA study**

Rømer, A.T. and Kreisel, A. and Eremin, I. and Malakhov, M.A. and Maier, T.A. and Hirschfeld, P.J. and Andersen, B.M.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two-dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to dx2-y2-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a Van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise subdominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time-reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasiparticle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet dx2-y2 gap as well as the chiral triplet gap solution. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.104505 **Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density wave**

Gradhand, M. and Eremin, I. and Knolle, J.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)We analyze the Hall conductivity σxy(ω) of a charge ordered state with momentum Q=(0,2Q) and calculate the intrinsic contribution to the Kerr angle ΘK using the fully reconstructed tight-binding band structure for layered cuprates beyond the low energy hot spot model and particle-hole symmetry. We show that such a unidirectional charge density wave (CDW), which breaks time-reversal symmetry, as recently put forward by Wang and Chubukov [Phys. Rev. B 90, 035149 (2014)PRBMDO1098-012110.1103/PhysRevB.90.035149], leads to a nonzero polar Kerr effect, as observed experimentally. In addition, we model a fluctuating CDW via a large quasiparticle damping of the order of the CDW gap and discuss possible implications for the pseudogap phase. We can qualitatively reproduce previous measurements of underdoped cuprates, but making quantitative connections to experiments is hampered by the sensitivity of the polar Kerr effect with respect to the complex refractive index n(ω). © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.060512 **Pressure-induced electronic phase separation of magnetism and superconductivity in CrAs**

Khasanov, R. and Guguchia, Z. and Eremin, I. and Luetkens, H. and Amato, A. and Biswas, P.K. and Rüegg, C. and Susner, M.A. and Sefat, A.S. and Zhigadlo, N.D. and Morenzoni, E.*Scientific Reports*5 (2015)The recent discovery of pressure (p) induced superconductivity in the binary helimagnet CrAs has raised questions on how superconductivity emerges from the magnetic state and on the mechanism of the superconducting pairing. In the present work the suppression of magnetism and the occurrence of superconductivity in CrAs were studied by means of muon spin rotation. The magnetism remains bulk up to p≃3.5 kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at p≃7 kbar. At 3.5 kbar superconductivity abruptly appears with its maximum T<inf>c</inf>≃1.2 K which decreases upon increasing the pressure. In the intermediate pressure region (3.5≲p≲7 kbar) the superconducting and the magnetic volume fractions are spatially phase separated and compete for phase volume. Our results indicate that the less conductive magnetic phase provides additional carriers (doping) to the superconducting parts of the CrAs sample thus leading to an increase of the transition temperature (T<inf>c</inf>) and of the superfluid density (ρ<inf>s</inf>). A scaling of ρ<inf>s</inf> with T<inf>c</inf>3.2 as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs. © 2015, NPG. All rights reserved.view abstract 10.1038/srep13788 **Robust determination of the superconducting gap sign structure via quasiparticle interference**

Hirschfeld, P.J. and Altenfeld, D. and Eremin, I. and Mazin, I.I.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)Phase-sensitive measurements of the superconducting gap in Fe-based superconductors have proven more difficult than originally anticipated. While quasiparticle interference (QPI) measurements based on scanning tunneling spectroscopy are often proposed as definitive tests of gap structure, the analysis typically relies on details of the model employed. Here we point out that the temperature dependence of momentum-integrated QPI data can be used to identify gap sign changes in a qualitative way, and present an illustration for s± and s++ states in a system with typical Fe-pnictide Fermi surface. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.184513 **Spin reorientation driven by the interplay between spin-orbit coupling and Hund's rule coupling in iron pnictides**

Christensen, M.H. and Kang, J. and Andersen, B.M. and Eremin, I. and Fernandes, R.M.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)In most magnetically-ordered iron pnictides, the magnetic moments lie in the FeAs planes, parallel to the modulation direction of the spin stripes. However, recent experiments in hole-doped iron pnictides have observed a reorientation of the magnetic moments from in-plane to out-of-plane. Interestingly, this reorientation is accompanied by a change in the magnetic ground state from a stripe antiferromagnet to a tetragonal nonuniform magnetic configuration. Motivated by these recent observations, here we investigate the origin of the spin anisotropy in iron pnictides using an itinerant microscopic electronic model that respects all the symmetry properties of a single FeAs plane. We find that the interplay between the spin-orbit coupling and the Hund's rule coupling can account for the observed spin anisotropies, including the spin reorientation in hole-doped pnictides, without the need to invoke orbital or nematic order. Our calculations also reveal an asymmetry between the magnetic ground states of electron- and hole-doped compounds, with only the latter displaying tetragonal magnetic states. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.214509 **Anisotropic softening of magnetic excitations along the nodal direction in superconducting cuprates**

Guarise, M. and Dalla Piazza, B. and Berger, H. and Giannini, E. and Schmitt, T. and Rønnow, H.M. and Sawatzky, G.A. and Van Den Brink, J. and Altenfeld, D. and Eremin, I. and Grioni, M.*Nature Communications*5 (2014)The high-Tc cuprate superconductors are close to antiferromagnetic order. Recent measurements of magnetic excitations have reported an intriguing similarity to the spin waves - magnons - of the antiferromagnetic insulating parent compounds, suggesting that magnons may survive in damped, broadened form throughout the phase diagram. Here we show by resonant inelastic X-ray scattering on Bi2Sr2CaCu2O8+δ (Bi-2212) that the analogy with spin waves is only partial. The magnon-like features collapse along the nodal direction in momentum space and exhibit a photon energy dependence markedly different from the Mott-insulating case. These observations can be naturally described by the continuum of charge and spin excitations of correlated electrons. The persistence of damped magnons could favour scenarios for superconductivity built from quasiparticles coupled to spin fluctuations. However, excitation spectra composed of particle-hole excitations suggest that superconductivity emerges from a coherent treatment of electronic spin and charge in the form of quasiparticles with very strong magnetic correlations. © 2014 Macmillan Publishers Limited. All rights reserved.view abstract 10.1038/ncomms6760 **Antiferromagnetism in iron-based superconductors: Magnetic order in the model of delocalized electrons**

Eremin, I.M.*Physics-Uspekhi*57 (2014)A theoretical analysis of the magnetic ordering mechanisms in parent ferropnictides (FPs) was investigated. The study takes into account that a ferropnictide remains metallic when it resides a magnetic state, and relies on a model that describes AFM order in terms of the spin density wave (SDW) for itinerant electrons. The reason is that optical conductivity measurements reveal a transfer of spectral weight from the Drude peak to the middle of the infrared peak, in accordance with the itinerant electron model that leads to AFM order. The SDW order parameter also becomes finite when the Fermi surface disappears. This results from the fact that an electron-hole loop formed by α and Β fermions is similar to the particle-particle loop because the α and Βband dispersions differ in sign. The calculated Fermi contours, ARPES spectral intensity, and the band dispersion near the Fermi level are consistent with the experimental data.view abstract 10.3367/UFNe.0184.201408g.0875 **Antiferromagnetism in iron-based superconductors: Selection of magnetic order and quasiparticle interference**

Eremin, I. and Knolle, J. and Fernandes, R.M. and Schmalian, J. and Chubukov, A.V.*Journal of the Physical Society of Japan*83 (2014)The recent discovery of superconductivity in the iron-based layered pnictides with Tc ranging between 26 and 56K generated enormous interest in the physics of these materials. Here, we review some of the peculiarities of the antiferromagnetic order in the iron pnictides, including the selection of the stripe magnetic order and the formation of the Ising-nematic state in the unfolded BZ within an itinerant description. In addition we analyze the properties of the quasiparticle interference spectrum in the parent antiferromagnetic phase. © 2014 The Physical Society of Japan.view abstract 10.7566/JPSJ.83.061015 **Magnetically driven suppression of nematic order in an iron-based superconductor**

Avci, S. and Chmaissem, O. and Allred, J.M. and Rosenkranz, S. and Eremin, I. and Chubukov, A.V. and Bugaris, D.E. and Chung, D.Y. and Kanatzidis, M.G. and Castellan, J.-P. and Schlueter, J.A. and Claus, H. and Khalyavin, D.D. and Manuel, P. and Daoud-Aladine, A. and Osborn, R.*Nature Communications*5 (2014)A theory of superconductivity in the iron-based materials requires an understanding of the phase diagram of the normal state. In these compounds, superconductivity emerges when stripe spin density wave (SDW) order is suppressed by doping, pressure or atomic disorder. This magnetic order is often pre-empted by nematic order, whose origin is yet to be resolved. One scenario is that nematic order is driven by orbital ordering of the iron 3d electrons that triggers stripe SDW order. Another is that magnetic interactions produce a spin-nematic phase, which then induces orbital order. Here we report the observation by neutron powder diffraction of an additional fourfold-symmetric phase in Ba 1 ̂'x Na x Fe 2 As 2 close to the suppression of SDW order, which is consistent with the predictions of magnetically driven models of nematic order.view abstract 10.1038/ncomms4845 **Model of nonadiabatic-to-adiabatic dynamical quantum phase transition in photoexcited systems**

Chang, J. and Eremin, I. and Zhao, J.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)We study the ultrafast dynamic process in photoexcited systems and find that the Franck-Condon or Landau-Zener tunneling between the photoexcited state and the ground state is abruptly blocked with increasing the state coupling from nonadiabatic to adiabatic limits. The blockage of the tunneling inhibits the photoexcited state from decaying into the thermalized state and results in an emergence of a metastable state, which represents an entanglement of electronic states with different electron-phonon coupling strengths. Applying this model to the investigation of photoexcited half-doped manganites, we show that the quantum critical transition is responsible for more than a three-order-of-magnitude difference in the ground-state recovery times following photoirradiation. This model also explains some elusive experimental results, such as photoinduced rearrangement of orbital order by the structural rather than electronic process and the structural bottleneck of a one-quarter period of the Jahn-Teller mode. We demonstrate that in the spin-boson model there exist unexplored regions not covered in the conventional phase diagram. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.104305 **Superconductivity from repulsion in LiFeAs: Novel s -wave symmetry and potential time-reversal symmetry breaking**

Ahn, F. and Eremin, I. and Knolle, J. and Zabolotnyy, V.B. and Borisenko, S.V. and Büchner, B. and Chubukov, A.V.*Physical Review B - Condensed Matter and Materials Physics*89 (2014)We analyze the structure of the pairing interaction and superconducting gap in LiFeAs by decomposing the pairing interaction for various kz cuts into s- and d-wave components and by studying the leading superconducting instabilities. We use the ten-orbital tight-binding model, derived from ab initio LDA calculations with hopping parameters extracted from the fit to ARPES experiments. We find that the pairing interaction almost decouples between two subsets; one consists of the outer hole pocket and two electron pockets, which are quasi-2D and are made largely out of the dxy orbital, and the other consists of the two inner hole pockets, which are quasi-3D and are made mostly out of dxz and dyz orbitals. Furthermore, the bare interpocket and intrapocket interactions within each subset are nearly equal. In this situation, small changes in the intrapocket and interpocket interactions due to renormalizations by high-energy fermions give rise to a variety of different gap structures. We focus on s-wave pairing which, as experiments show, is the most likely pairing symmetry in LiFeAs. We find four different configurations of the s-wave gap immediately below Tc: one in which the superconducting gap changes sign between two inner hole pockets and between the outer hole pocket and two electron pockets, one in which the gap changes sign between two electron pockets and three hole pockets, one in which the gap on the outer hole pocket differs in sign from the gaps on the other four pockets, and one in which the gaps on two inner hole pockets have one sign and the gaps on the outer hole pockets and on electron pockets have different sign. Different s-wave gap configurations emerge depending on whether the renormalized interactions increase attraction within each subset or increase the coupling between particular components of the two subsets. We discuss the phase diagram and experimental probes to determine the structure of the superconducting gap in LiFeAs. We argue that the state with opposite sign of the gaps on the two inner hole pockets has the best overlap with ARPES data. We also argue that at low T, the system may enter into a "mixed" s+is state, in which the phases of the gaps on different pockets differ by less than π and time-reversal symmetry is spontaneously broken. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.89.144513 **Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetism**

Nogueira, F.S. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)Motivated by recent experiments on EuS/Bi2Se3 heterostructures, we study the temperature dependent screening effects on the surface of a three-dimensional topological insulator proximate to a ferromagnetically ordered system. In general, we find that besides the chemical potential and temperature, the screening energy scale also depends on the proximity-induced electronic gap in an essential way. In particular, at zero temperature the screening energy vanishes if the chemical potential is smaller than the proximity-induced electronic gap. We show that at finite temperature T and/or chemical potential, the Chern-Simons (topological) mass, which is generated by quantum fluctuations arising from the proximity effect, can be calculated analytically in the insulating regime. In this case the topological mass yields the Hall conductivity associated with edge states. We show that when the chemical potential is inside the gap the topological mass remains nearly quantized at finite temperature. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.014431 **Ultrafast modulation of the chemical potential in BaFe2As2 by coherent phonons**

Yang, L.X. and Rohde, G. and Rohwer, T. and Stange, A. and Hanff, K. and Sohrt, C. and Rettig, L. and Cortés, R. and Chen, F. and Feng, D.L. and Wolf, T. and Kamble, B. and Eremin, I. and Popmintchev, T. and Murnane, M.M. and Kapteyn, H.C. and Kipp, L. and Fink, J. and Bauer, M. and Bovensiepen, U. and Rossnagel, K.*Physical Review Letters*112 (2014)Time- and angle-resolved extreme ultraviolet photoemission spectroscopy is used to study the electronic structure dynamics in BaFe2As2 around the high-symmetry points Γ and M. A global oscillation of the Fermi level at the frequency of the A1g(As) phonon mode is observed. It is argued that this behavior reflects a modulation of the effective chemical potential in the photoexcited surface region that arises from the high sensitivity of the band structure near the Fermi level to the A1g(As) phonon mode combined with a low electron diffusivity perpendicular to the layers. The results establish a novel way to tune the electronic properties of iron pnictides: coherent control of the effective chemical potential. The results further suggest that the equilibration time for the effective chemical potential needs to be considered in the ultrafast electronic structure dynamics of materials with weak interlayer coupling. © 2014 American Physical Society.view abstract 10.1103/PhysRevLett.112.207001 **Evolution of the multiband Ruderman-Kittel-Kasuya-Yosida interaction: Application to iron pnictides and chalcogenides**

Akbari, A. and Thalmeier, P. and Eremin, I.*New Journal of Physics*15 (2013)The indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in iron pnictide and chalcogenide metals is calculated for a simplified four-band Fermi surface model. We investigate the specific multi-band features and show that distinct length scales of the RKKY oscillations appear. For the regular lattice of local moments, the generalized RKKY interaction is defined in momentum space. We consider its momentum dependence in paramagnetic and spin density wave phases, discuss its implications for the possible type of magnetic order and compare it with the results obtained from a more realistic tight-binding-type Fermi surface model. Our finding can give important clues to the magnetic ordering of 4f-iron-based superconductors. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/3/033034 **Semimetal-insulator transition on the surface of a topological insulator with in-plane magnetization**

Nogueira, F.S. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*88 (2013)A thin film of ferromagnetically ordered material proximate to the surface of a three-dimensional topological insulator explicitly breaks the time-reversal symmetry of the surface states. For an out-of-plane ferromagnetic order parameter on the surface, the parity is also broken since the Dirac fermions become massive. This leads, in turn, to the generation of a topological Chern-Simons term by quantum fluctuations. On the other hand, for an in-plane magnetization the surface states remain gapless for the noninteracting Dirac fermions. In this work we study the possibility of spontaneous breaking of parity due to a dynamical gap generation on the surface in the presence of a local, Hubbard-like interaction of strength g between the Dirac fermions. A gap and a Chern-Simons term are generated for g larger than some critical value gc, provided the number of Dirac fermions N is odd. For an even number of Dirac fermions the masses are generated in pairs having opposite signs, and no Chern-Simons term is generated. We discuss our results in the context of recent experiments in EuS/Bi2Se3 heterostructures. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.88.085126 **Spin-orbit coupling in Fe-based superconductors**

Korshunov, M.M. and Togushova, Y.N. and Eremin, I. and Hirschfeld, P.J.*Journal of Superconductivity and Novel Magnetism*26 (2013)We study the spin resonance peak in recently discovered iron-based superconductors. The resonance peak observed in inelastic neutron scattering experiments agrees well with predicted results for the extended s-wave (s ±) gap symmetry. Recent neutron scattering measurements show that there is a disparity between transverse and longitudinal components of the dynamical spin susceptibility. Such breaking of the spin-rotational invariance in the spin-liquid phase can occur due to spin-orbit coupling. We study the role of the spin-orbit interaction in the multiorbital model for Fe-pnictides and show how it affects the spin resonance feature. © 2013 Springer Science+Business Media New York.view abstract 10.1007/s10948-013-2212-6 **Theory of nonequilibrium dynamics of multiband superconductors**

Akbari, A. and Schnyder, A.P. and Manske, D. and Eremin, I.*EPL*101 (2013)We study the nonequilibrium dynamics of multiband BCS superconductors subjected to ultrashort pump pulses. Using density-matrix theory, the time evolution of the Bogoliubov quasiparticle densities and the superconducting order parameters are computed as a function of pump pulse frequency, duration, and intensity. Focusing on two-band superconductors, we consider two different model systems. The first one, relevant for iron-based superconductors, describes two-band superconductors with a repulsive interband interaction V12 which is much larger than the intraband pairing terms. The second model, relevant for MgB2, deals with the opposite limit where the intraband interactions are dominant and the interband pair scattering V12 is weak but attractive. For ultrashort pump pulses, both of these models exhibit a nonadiabatic behavior which is characterized by oscillations of the superconducting order parameters. We find that for nonvanishing V12, the superconducting gap on each band exhibits two oscillatory frequencies which are determined by the long-time asymptotic values of the gaps. The relative strength of these two frequency components depends sensitively on the magnitude of the interband interaction V12. © Copyright EPLA, 2013.view abstract 10.1209/0295-5075/101/17002 **Three-orbital model for Fe-pnictides**

Korshunov, M.M. and Togushova, Y.N. and Eremin, I.*Journal of Superconductivity and Novel Magnetism*26 (2013)We formulate and study the three-orbital model for iron-based superconductors. Results for the band structure, Fermi surface, and the spin susceptibility in both normal and superconducting s ± states are presented. We also discuss the pairing interaction and show that the dominant part of it should come from the intraorbital scattering. © 2013 Springer Science+Business Media New York.view abstract 10.1007/s10948-013-2156-x **Dual features of magnetic susceptibility in superconducting cuprates: A comparison to inelastic neutron scattering**

Eremin, M.V. and Shigapov, I.M. and Eremin, I.M.*European Physical Journal B*85 (2012)Starting from the generalized t-J-G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. We demonstrate that derived expression reproduces the basic observations of neutron scattering data in YBa 2Cu 3O 6+y compounds near the optimal doping level. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.view abstract 10.1140/epjb/e2012-20539-y **Fluctuation-induced magnetization dynamics and criticality at the interface of a topological insulator with a magnetically ordered layer**

Nogueira, F.S. and Eremin, I.*Physical Review Letters*109 (2012)We consider a theory for a two-dimensional interacting conduction electron system with strong spin-orbit coupling on the interface between a topological insulator and the magnetic (ferromagnetic or antiferromagnetic) layer. For the ferromagnetic case we derive the Landau-Lifshitz equation, which features a contribution proportional to a fluctuation-induced electric field obtained by computing the topological (Chern-Simons) contribution from the vacuum polarization. We also show that fermionic quantum fluctuations reduce the critical temperature Tc at the interface relative to the critical temperature Tc of the bulk, so that in the interval T c≤T< Tc it is possible to have a coexistence of gapless Dirac fermions at the interface with a ferromagnetically ordered layer. For the case of an antiferromagnetic layer on a topological insulator substrate, we show that a second-order quantum phase transition occurs at the interface, and compute the corresponding critical exponents. In particular, we show that the electrons at the interface acquire an anomalous dimension at criticality. The critical behavior of the Néel order parameter is anisotropic and features large anomalous dimensions for both the longitudinal and transversal fluctuations. © 2012 American Physical Society.view abstract 10.1103/PhysRevLett.109.237203 **Incommensurate magnetic fluctuations and Fermi surface topology in LiFeAs**

Knolle, J. and Zabolotnyy, V.B. and Eremin, I. and Borisenko, S.V. and Qureshi, N. and Braden, M. and Evtushinsky, D.V. and Kim, T.K. and Kordyuk, A.A. and Sykora, S. and Hess, C. and Morozov, I.V. and Wurmehl, S. and Moessner, R. and Büchner, B.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)Using the angle-resolved photoemission spectroscopy data accumulated over the whole Brillouin zone (BZ) in LiFeAs, we analyze the itinerant component of the dynamic spin susceptibility in this system in the normal and superconducting state. We identify the origin of the incommensurate magnetic inelastic neutron scattering (INS) intensity as scattering between the electron pockets, centered around the (π,π) point of the BZ, and the large two-dimensional hole pocket, centered around the Γ point of the BZ. As the magnitude of the superconducting gap within the large hole pocket is relatively small and angle dependent, we interpret the INS data in the superconducting state as a renormalization of the particle-hole continuum rather than a true spin exciton. Our comparison indicates that the INS data can be reasonably well described by both the sign-changing symmetry of the superconducting gap between electron and hole pockets and the sign-preserving gap, depending on the assumptions made for the fermionic damping. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.174519 **Preemptive nematic order, pseudogap, and orbital order in the iron pnictides**

Fernandes, R.M. and Chubukov, A.V. and Knolle, J. and Eremin, I. and Schmalian, J.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)Starting from a microscopic itinerant model, we derive and analyze the effective low-energy model for collective magnetic excitations in the iron pnictides. We show that the stripe magnetic order is generally preempted by an Ising-nematic order, which breaks C 4 lattice symmetry but preserves O(3) spin-rotational symmetry. This leads to a rich phase diagram as function of doping, pressure, and elastic moduli, displaying split magnetic and nematic tricritical points. The nematic transition may instantly bring the system to the verge of a magnetic transition, or it may occur first, being followed by a magnetic transition at a lower temperature. In the latter case, the preemptive nematic transition is accompanied by either a jump or a rapid increase of the magnetic correlation length, triggering a pseudogap behavior associated with magnetic precursors. Furthermore, due to the distinct orbital character of each Fermi pocket, the nematic transition also induces orbital order. We compare our results to various experiments, showing that they correctly address the changes in the character of the magnetostructural transition across the phase diagrams of different compounds, as well as the relationship between the orthorhombic and magnetic order parameters. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.024534 **Spin excitations in layered antiferromagnetic metals and superconductors**

Rowe, W. and Knolle, J. and Eremin, I. and Hirschfeld, P.J.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)The proximity of antiferromagnetic order in high-temperature superconducting materials is considered a possible clue to the electronic excitations which form superconducting pairs. Here we study the transverse and longitudinal spin excitation spectrum in a one-band model in the pure spin density wave (SDW) state and in the coexistence state of SDW and the superconductivity. We start from a Stoner insulator and study the evolution of the spectrum with doping, including distinct situations with only hole pockets, with only electron pockets, and with pockets of both types. In addition to the usual spin-wave modes, in the partially gapped cases we find significant weight of low-energy particle-hole excitations. We discuss the implications of our findings for neutron scattering experiments and for theories of Cooper pairing in the metallic SDW state. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.134513 **Strong-coupling topological Josephson effect in quantum wires**

Nogueira, F.S. and Eremin, I.*Journal of Physics Condensed Matter*24 (2012)We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling regime, the exact solution reproduces the perturbative result for the energy containing a contribution ±cos(/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value . At this point the Josephson energies have the principal values , where m=1,0,1 and σ=±1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with an odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels. © 2012 IOP Publishing Ltd.view abstract 10.1088/0953-8984/24/32/325701 **The antiferromagnetic phase of iron-based superconductors: An itinerant approach**

Knolle, J. and Eremin, I.*Iron-based Superconductors: Materials, Properties and Mechanisms*(2012)view abstract 10.4032/9789814303231 **Effect of fermi surface nesting on resonant spin excitations in Ba 1-xKxFe2As2**

Castellan, J.-P. and Rosenkranz, S. and Goremychkin, E.A. and Chung, D.Y. and Todorov, I.S. and Kanatzidis, M.G. and Eremin, I. and Knolle, J. and Chubukov, A.V. and Maiti, S. and Norman, M.R. and Weber, F. and Claus, H. and Guidi, T. and Bewley, R.I. and Osborn, R.*Physical Review Letters*107 (2011)We report inelastic neutron scattering measurements of the resonant spin excitations in Ba1-xKxFe2As2 over a broad range of electron band filling. The fall in the superconducting transition temperature with hole doping coincides with the magnetic excitations splitting into two incommensurate peaks because of the growing mismatch in the hole and electron Fermi surface volumes, as confirmed by a tight-binding model with s±-symmetry pairing. The reduction in Fermi surface nesting is accompanied by a collapse of the resonance binding energy and its spectral weight, caused by the weakening of electron-electron correlations. © 2011 American Physical Society.view abstract 10.1103/PhysRevLett.107.177003 **Effect of nodes, ellipticity, and impurities on the spin resonance in iron-based superconductors**

Maiti, S. and Knolle, J. and Eremin, I. and Chubukov, A.V.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We analyze doping dependence of the spin resonance of an s ± superconductor and its sensitivity to the ellipticity of electron pockets, to magnetic and nonmagnetic impurities, and to the angle dependence of the superconducting gap along electron Fermi surfaces. We show that the maximum intensity of the resonance shifts from commensurate to incommensurate momentum above some critical doping which decreases with increasing ellipticity. Angle dependence of the gap and particularly the presence of accidental nodes lowers the overall intensity of the resonance peak and shifts its position toward the onset of the particle-hole continuum. Still, however, the resonance remains a true δ function in the clean limit. When nonmagnetic or magnetic impurities are present, the resonance broadens and its position shifts. The shift depends on the type of impurities and on the ratio of intraband and interband scattering components. The ratio Ωres/ Tc increases almost linearly with the strength of the interband impurity scattering, in agreement with the experimental data. We also compare spin response of s± and s++ superconductors. We show that there is no resonance for s+ + gap, even when there is a finite mismatch between electron and hole Fermi surfaces shifted by the antiferromagnetic momentum. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.144524 **Magnetic rare-earth impurity resonance bound states in iron-based superconductors**

Akbari, A. and Thalmeier, P. and Eremin, I.*Journal of Superconductivity and Novel Magnetism*24 (2011)Starting from an Anderson model for two-orbital model of electron and hole conduction bands which hybridized with the localized impurity spin, we investigate the effect of magnetic impurities on the local quasiparticle density of states (LDOS) in iron-based superconductors. We consider extended s-wave (s +-) superconducting gap symmetry with higher harmonic correction. The impurity-induced bound states are a probe for the nodal structure of the extended s-wave symmetry in ferropnictides. © 2010 Springer Science+Business Media, LLC.view abstract 10.1007/s10948-010-1103-3 **Magnetic resonance from the interplay of frustration and superconductivity**

Knolle, J. and Eremin, I. and Schmalian, J. and Moessner, R.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)Motivated by iron-based superconductors, we develop a self-consistent electronic theory for the itinerant spin excitations in the regime of coexistence of the antiferromagnetic stripe order with wave vector Q 1=(π,0) and s+- superconductivity. The onset of superconductivity leads to the appearance of a magnetic resonance near the wave vector Q2=(0,π), where magnetic order is absent. This resonance is isotropic in spin space, unlike the excitations near Q1, where the magnetic Goldstone mode resides. We discuss several features which can be observed experimentally. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.180510 **Multiorbital spin susceptibility in a magnetically ordered state: Orbital versus excitonic spin density wave scenario**

Knolle, J. and Eremin, I. and Moessner, R.*Physical Review B - Condensed Matter and Materials Physics*83 (2011)We present a general theory of multiorbital spin waves in magnetically ordered metallic systems. Motivated by the itinerant magnetism of iron-based superconductors, we compare the magnetic excitations for two different scenarios: when the magnetic order either sets in on the on-site orbital level; or when it appears as an electron-hole pairing between different bands of electron and hole characters. As an example, we treat the two-orbital model for iron-based superconductors. For small magnetic moments the spin excitations look similar in both scenarios. Going to larger interactions and larger magnetic moments, the difference between both scenarios becomes striking. While in the excitonic scenario the spin waves form a closed structure over the entire Brillouin zone and the particle-hole continuum is gapped, the spin excitations in the orbital scenario can be treated as spin waves only in a close vicinity to the ordering momenta. The origin of this is a gapless electronic structure with Dirac cones which is a source of large damping. We analyze our results in connection with recent neutron scattering measurements and show that certain features of the orbital scenario with multiple order parameters can be observed experimentally. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.83.224503 **Particlehole asymmetry as a source of phase separation at the metalinsulator transition**

Karnaukhov, I.N. and Eremin, I.*Journal of Physics A: Mathematical and Theoretical*44 (2011)We propose a strongly correlated (1+1)D electron model with particlehole asymmetry which is exactly solvable by means of the nested Bethe ansatz. The particlehole asymmetry in this many-body system causes a metalinsulator transition with a phase separation. Here, we give a detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual behavior of the metalinsulator transition with phase separation arises. In particular, we show that a homogeneous phase of itinerant electrons and a mixed phase of itinerant electrons and localized electron pairs (for which two different species reside in spatially separated regions) define the ground state of a fermion chain. We also find that the metalinsulator phase transition induces phase transition on the surface with simultaneous generation of the interphase boundary. © 2011 IOP Publishing Ltd.view abstract 10.1088/1751-8113/44/39/395002 **Quasiparticle interference in the heavy-fermion superconductor CeCoIn 5**

Akbari, A. and Thalmeier, P. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We investigate the quasiparticle interference in the heavy fermion superconductor CeCoIn 5 as a direct method to confirm the d-wave gap symmetry. The ambiguity between d xy and d x2-y2 symmetry remaining from earlier specific heat and thermal transport investigations has been resolved in favor of the latter by the observation of a spin resonance that can occur only in d x2-y2 symmetry. However, these methods are all indirect and depend considerably on theoretical interpretation. Here we propose that quasiparticle interference (QPI) spectroscopy by scanning tunneling microscopy (STM) can give a direct fingerprint of the superconducting gap in real space that may lead to a definite conclusion on its symmetry for CeCoIn 5 and related 115 compounds. The QPI pattern for both magnetic and nonmagnetic impurities is calculated for the possible d-wave symmetries and characteristic differences are found that may be identified by use of the STM method. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.134505 **RKKY interaction in the spin-density-wave phase of iron-based superconductors**

Akbari, A. and Eremin, I. and Thalmeier, P.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)Using the multiband model we analyze the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the magnetic impurities in layered ferropnictide superconductors. In the normal state the interaction is spin isotropic and is dominated by the nesting features of the electron and hole bands separated by the antiferromagnetic (AF) momentum, Q AF. In the AF state the RKKY interaction maps into an effective anisotropic XXZ-type Heisenberg exchange model. The anisotropy originates from the breaking of the spin-rotational symmetry induced by the AF order and its strength depends on the size of the AF gap and the structure of the folded Fermi surface. We discuss our results in connection with recent experiments. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.134513 **Angle-resolved specific heat in iron-based superconductors: The case for a nodeless extended s-wave gap**

Chubukov, A.V. and Eremin, I.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We consider the variation in the field-induced component of the specific heat C (H) with the direction of the applied field in Fe pnictides within quasiclassical Doppler-shift approximation with special emphasis to recent experiments on FeSe0.4 Te0.6. We show that for extended s -wave gap with no nodes, C (H) has cos4 component, where is the angle between H and the direction between hole and electron Fermi surfaces. The maxima of C (H) are at π/4, 3π/4, etc., if the applied field is smaller than H0 ≤1T, and at =0, π/2, etc., if the applied field is larger than H0. The angle dependence of C (H), the positions of the maxima, and the relative magnitude of the oscillating component are consistent with the experiments performed in the field of 9TH0. We show that the observed cos4 variation does not hold if the s -wave gap has accidental nodes along the two electron Fermi surfaces. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.060504 **Feedback effect on spin excitations in Ce-based unconventional superconductors**

Thalmeier, P. and Akbari, A. and Eremin, I.*Physica C: Superconductivity and its Applications*470 (2010)The feedback resonance in inelastic neutron scattering (INS) is observed in CeCu2Si2 and CeCoIn5. Below T c the gap opening may lead to a dispersive spin exciton with an energy ωr/2Δ0< 1. Observation of this collective mode at magnetic wave vector Q requires Δ(k+Q)=-Δ(k) which allows to conclude a dx2-y2 gap symmetry for both Ce compounds. A different kind of feedback was observed in the Ce-based ferropnictides. The transition between crystalline electric field (CEF) split Ce-4f states has anomalous shift and linewidth which is explained as an effect of coupling to resonant 3d spin excitations below Tc giving evidence for a s± state. © 2009 Elsevier B.V. All rights reserved.view abstract 10.1016/j.physc.2009.11.036 **Feedback spin exciton formation in unconventional superconductors**

Thalmeier, P. and Eremin, I. and Akbari, A. and Fulde, P.*Journal of Superconductivity and Novel Magnetism*23 (2010)The superconducting feedback resonance in inelastic neutron scattering (INS) has now been found in numerous unconventional superconductors of the cuprate, ferropnictide, and heavy fermion classes. The collective spin excitation appears below T c at an energy less than the quasiparticle threshold with momentum Q provided the gap changes sign under translation by Q. The resonance has been found in the heavy fermion (HF) superconductors CeCu 2Si 2, CeCoIn 5, and UPd 2Al 3, and recently in Fe-pnictide Ba 1-xK xFe 2As 2, BaFe 2-xCo xAs 2, BaFe 2-xNi xAs 2, and FeSe 1-xTe x compounds and may be a more general phenomenon. Of particular interest is the interaction of the 3d spin exciton with the 4f crystalline electric field (CEF) excitations in rare earth based unconventional superconductors like CeFeAsO 1-xF x pnictide and Nd 2-xCe xCuO 4 cuprate where a coupling between 3d spin resonance and 4f CEF excitations leads to intriguing interaction effects observed experimentally by INS. © The Author(s) 2010.view abstract 10.1007/s10948-010-0646-7 **Incommensurate itinerant antiferromagnetic excitations and spin resonance in the FeTe0.6Se0.4 superconductor**

Argyriou, D.N. and Hiess, A. and Akbari, A. and Eremin, I. and Korshunov, M.M. and Hu, J. and Qian, B. and Mao, Z. and Qiu, Y. and Broholm, C. and Bao, W.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We report on inelastic neutron-scattering measurements that find itinerantlike incommensurate magnetic excitations in the normal state of superconducting FeTe0.6Se0.4 (Tc =14 K) at wave vector Qinc = (1/2±, ε 1/2 ε) with ε=0.09 (1). In the superconducting state only the lower energy part of the spectrum shows significant changes by the formation of a gap and a magnetic resonance that follows the dispersion of the normal-state excitations. We use a four band model to describe the Fermi-surface topology of this iron-based superconductors with the extended s (±) symmetry and find that it qualitatively captures the salient features of these data. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.220503 **Interplay of magnetic and structural transitions in iron-based pnictide superconductors**

Cano, A. and Civelli, M. and Eremin, I. and Paul, I.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)The interplay between the structural and magnetic phase transitions occurring in the Fe-based pnictide superconductors is studied within a Ginzburg-Landau approach. We show that the magnetoelastic coupling between the corresponding order parameters is behind the salient features observed in the phase diagram of these systems. This naturally explains the coincidence of transition temperatures observed in some cases as well as the character (first or second order) of the transitions. We also show that magnetoelastic coupling is the key ingredient determining the collinearity of the magnetic ordering and we propose an experimental criterion to distinguish between a pure elastic from a spin-nematic-driven structural transition. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.020408 **Magnetic degeneracy and hidden metallicity of the spin-density-wave state in ferropnictides**

Eremin, I. and Chubukov, A.V.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We analyze spin-density-wave (SDW) order in iron-based superconductors and electronic structure in the SDW phase. We consider an itinerant model for Fe pnictides with two hole bands centered at (0,0) and two electron bands centered at (0,π) and (π,0) in the unfolded Brillouin zone. A SDW order in such a model is generally a combination of two components with momenta (0,π) and (π,0), both yield (π,π) order in the folded zone. Neutron experiments, however, indicate that only one component is present. We show that (0,π) or (π,0) order is selected if we assume that only one hole band is involved in the SDW mixing with electron bands. A SDW order in such three-band model is highly degenerate for a perfect nesting and hole-electron interaction only but we show that ellipticity of electron pockets and interactions between electron bands break the degeneracy and favor the desired (0,π) or (π,0) order. We further show that stripe-ordered system remains a metal for arbitrary coupling. We analyze electronic structure for parameters relevant to the pnictides and argue that the resulting electronic structure is in good agreement with angle-resolved photoemission experiments. We discuss the differences between our model and J1 - J2 model of localized spins. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.024511 **Magnetic impurity resonance states and symmetry of the superconducting order parameter in iron-based superconductors**

Akbari, A. and Eremin, I. and Thalmeier, P.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We investigate the effect of magnetic impurities on the local quasiparticle density of states in iron-based superconductors. Employing the two-orbital model where 3d electron and hole conduction bands are hybridizing with the localized f orbital of the impurity spin, we investigate how various symmetries of the superconducting gap and its nodal structure influence the quasiparticle excitations and impurity bound states. We show that the bound states behave qualitatively different for each symmetry. Most importantly we find that the impurity-induced bound states can be used to identify the nodal structure of the extended s -wave symmetry (S±) that is actively discussed in ferropnictides. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.014524 **Pair breaking by nonmagnetic impurities in the noncentrosymmetric superconductor CePt3 Si**

Nicklas, M. and Steglich, F. and Knolle, J. and Eremin, I. and Lackner, R. and Bauer, E.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We have studied the effect of Ge substitution and pressure on the heavy-fermion superconductor CePt3 Si. Ge substitution on the Si site acts as negative chemical pressure leading to an increase in the unit-cell volume but also introduces chemical disorder. We carried out electrical resistivity and ac heat-capacity experiments under hydrostatic pressure on CePt3 Si1-x Gex (x=0,0.06). Our experiments show that the suppression of superconductivity in CePt3 Si 1-x Gex is mainly caused by the scattering potential, rather than volume expansion, introduced by the Ge dopants. The antiferromagnetic order is essentially not affected by the chemical disorder. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.180511 **Quasiparticle interference in iron-based superconductors**

Akbari, A. and Knolle, J. and Eremin, I. and Moessner, R.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We systematically calculate quasiparticle interference (QPI) signatures for the whole phase diagram of iron-based superconductors. Impurities inherent in the sample together with ordered phases lead to distinct features in the QPI images that are believed to be measured in spectroscopic imaging-scanning tunneling microscopy. In the spin-density wave phase the rotational symmetry of the electronic structure is broken, signatures of which are also seen in the coexistence regime with both superconducting and magnetic order. In the superconducting regime we show how the different scattering behavior for magnetic and nonmagnetic impurities allows to verify the s⊃+⊃- symmetry of the order parameter. The effect of possible gap minima or nodes is discussed. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.224506 **Quasiparticle interference in the spin-density wave phase of iron-based superconductors**

Knolle, J. and Eremin, I. and Akbari, A. and Moessner, R.*Physical Review Letters*104 (2010)We propose an explanation for the electronic nematic state observed recently in parent iron-based superconductors. We argue that the quasi-one-dimensional nanostructure identified in the quasiparticle interference (QPI) is a consequence of the interplay of the magnetic (π, 0) spin-density wave (SDW) order with the underlying electronic structure. We show that the evolution of the QPI peaks largely reflects quasiparticle scattering between bands involved in the SDW formation. Because of the ellipticity of the electron pocket and the fact that only one of the electron pockets is involved in the SDW, the resulting QPI has a pronounced one-dimensional structure. We further predict that the QPI crosses over to two dimensionality on an energy scale, set by the SDW gap. © 2010 The American Physical Society.view abstract 10.1103/PhysRevLett.104.257001 **Self-energy effects and electron-phonon coupling in Fe-As superconductors**

Choi, K.-Y. and Lemmens, P. and Eremin, I. and Zwicknagl, G. and Berger, H. and Sun, G.L. and Sun, D.L. and Lin, C.T.*Journal of Physics Condensed Matter*22 (2010)Doping and temperature dependent studies of optical phonon modes in Fe-122 pnictides are performed using Raman scattering experiments and compared with model calculations to elucidate the role of electron-phonon and spin-phonon interaction in this family of compounds. The frequency and linewidth of the B1g mode at around 210cm-1 is highlighted as appreciable anomalies at the superconducting and spin density wave transitions are observed that strongly depend on composition. We give estimates of the electron-phonon coupling related to this renormalization and calculate the phonon self-energy on the basis of a four-band model comparing different symmetries of the order parameters. In addition, we observe a pronounced quasi-elastic Raman response for the undoped compound, suggesting persisting magnetic fluctuations in the spin density wave state. © 2010 IOP Publishing Ltd.view abstract 10.1088/0953-8984/22/11/115802 **Theory of itinerant magnetic excitations in the spin-density-wave phase of iron-based superconductors**

Knolle, J. and Eremin, I. and Chubukov, A.V. and Moessner, R.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We argue that salient experimental features of the magnetic excitations in the spin-density-wave phase of iron-based superconductors can be understood within an itinerant model. We identify a minimal model and use a multiband random-phase approximation treatment of the dynamical spin susceptibility. Weakly damped spin waves are found near the ordering momentum and it is shown how they dissolve into the particle-hole continuum. We show that ellipticity of the electron bands accounts for the anisotropy of the spin waves along different crystallographic directions and the spectral gap at the momentum conjugated to the ordering one. We argue that our theory agrees well with the existing neutron scattering data. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.140506 **Theory of multiband superconductivity in Spin-density-wave metals**

Ismer, J.-P. and Eremin, I. and Rossi, E. and Morr, D.K. and Blumberg, G.*Physical Review Letters*105 (2010)We study the emergence of multiband superconductivity with s- and d-wave symmetry on the background of a spin density wave (SDW). We show that the SDW coherence factors renormalize the momentum dependence of the superconducting (SC) gap, yielding a SC state with an unconventional s-wave symmetry. Interband Cooper pair scattering stabilizes superconductivity in both symmetries. With increasing SDW order, the s-wave state is more strongly suppressed than the d-wave state. Our results are universally applicable to two-dimensional systems with a commensurate SDW. © 2010 The American Physical Society.view abstract 10.1103/PhysRevLett.105.037003 **Unusual disorder effects in superconducting LaFeAs1-δ O0.9 F0.1 as revealed by 75As NMR spectroscopy**

Hammerath, F. and Drechsler, S.-L. and Grafe, H.-J. and Lang, G. and Fuchs, G. and Behr, G. and Eremin, I. and Korshunov, M.M. and Büchner, B.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We report 75As nuclear magnetic resonance measurements of the spin-lattice relaxation in the superconducting (SC) state of LaFeAsO 0.9F0.1 and As-deficient LaFeAs1-δO 0.9F0.1. The temperature behavior of 1/T1 below Tc changes drastically from a T3 dependence for LaFeAsO0.9F0.1 to a T5 dependence for the As-deficient sample. These results, together with the previously reported unexpected increase in Tc and the slope of the upper critical field near Tc for the As-deficient sample, are discussed in terms of nonuniversal SC gaps in Fe pnictides and the effect of As deficiency as an exotic case where nonmagnetic "smart" impurities even stabilize an s±-wave superconductor or within a scenario of a disorder-driven change to s++ superconductivity. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.140504

#### electronic structure

#### magnetism

#### short-time dynamics

#### superconductors

#### topological insulators