#### Prof. Dr. Jürgen König

Electronic and Magnetic Properties of Many Body Systems

University of Duisburg-Essen

##### Contact

- koenig[at]thp[dot]uni-due[dot]de
- +49 203 379 3329
- personal website

##### Author IDs

- ORCID: 0000-0003-3836-4611
- Scopus: 7102062567

##### Hub

**Environment-induced decay dynamics of antiferromagnetic order in Mott-Hubbard systems**

Schaller, G. and Queisser, F. and Szpak, N. and König, J. and Schützhold, R.*Physical Review B*105 (2022)We study the dissipative Fermi-Hubbard model in the limit of weak tunneling and strong repulsive interactions, where each lattice site is tunnel-coupled to a Markovian fermionic bath. For cold baths at intermediate chemical potentials, the Mott insulator property remains stable and we find a fast relaxation of the particle number towards half filling. On longer time scales, we find that the antiferromagnetic order of the Mott-Néel ground state on bipartite lattices decays, even at zero temperature. For zero and nonzero temperatures, we quantify the different relaxation time scales by means of waiting time distributions, which can be derived from an effective (non-Hermitian) Hamiltonian and obtain fully analytic expressions for the Fermi-Hubbard model on a tetramer ring. © 2022 American Physical Society.view abstract 10.1103/PhysRevB.105.115139 **Pushing the Limits in Real-Time Measurements of Quantum Dynamics**

Kleinherbers, E. and Stegmann, P. and Kurzmann, A. and Geller, M. and Lorke, A. and König, J.*Physical Review Letters*128 (2022)Time-resolved studies of quantum systems are the key to understanding quantum dynamics at its core. The real-time measurement of individual quantum numbers as they switch between certain discrete values, well known as a "random telegraph signal,"is expected to yield maximal physical insight. However, the signal suffers from both systematic errors, such as a limited time resolution and noise from the measurement apparatus, as well as statistical errors due to a limited amount of data. Here we demonstrate that an evaluation scheme based on factorial cumulants can reduce the influence of such errors by orders of magnitude. The error resilience is supported by a general theory for the detection errors as well as experimental data of single-electron tunneling through a self-assembled quantum dot. Thus, factorial cumulants push the limits in the analysis of random telegraph data, which represent a wide class of experiments in physics, chemistry, engineering, and life sciences. © 2022 American Physical Society.view abstract 10.1103/PhysRevLett.128.087701 **Quantum Zeno manipulation of quantum dots**

Ahmadiniaz, N. and Geller, M. and König, J. and Kratzer, P. and Lorke, A. and Schaller, G. and Schützhold, R.*Physical Review Research*4 (2022)view abstract 10.1103/PhysRevResearch.4.L032045 **Transfer-matrix summation of path integrals for transport through nanostructures**

Mundinar, S. and Hahn, A. and König, J. and Hucht, A.*Physical Review B*106 (2022)On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme to a transfer-matrix approach, which is more accessible to physical interpretation, allows for a more transparent formulation of the theory, and substantially improves the efficiency. In particular, the stationary limit is directly implemented, without the need of extrapolation. The resulting method, referred to as "transfer-matrix summation of path integrals"(TraSPI), is then applied to resonant electronic transport through a single-level quantum dot. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.view abstract 10.1103/PhysRevB.106.165427 **Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes**

Stegmann, P. and Sothmann, B. and König, J. and Flindt, C.*Physical Review Letters*127 (2021)Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid. © 2021 American Physical Society.view abstract 10.1103/PhysRevLett.127.096803 **How to get from static to dynamic electromagnetism**

König, J.*European Journal of Physics*42 (2021)We demonstrate how to derive Maxwell’s equations, including Faraday’s law and Maxwell’s correction to Ampère’s law, by generalizing the description of static electromagnetism to dynamical situations. Thereby, Faraday’s law is introduced as a consequence of the relativity principle rather than an experimental fact, in contrast to the historical course and common textbook presentations. As a by-product, this procedure yields explicit expressions for the infinitesimal Lorentz and, upon integration, the finite Lorentz transformation. The proposed approach helps to elucidate the relation between Galilei and Lorentz transformations and provides an alternative derivation of the Lorentz transformation without explicitly referring to the speed of light. © 2021 European Physical Societyview abstract 10.1088/1361-6404/abee60 **Newton series expansion of bosonic operator functions**

König, J. and Hucht, A.*SciPost Physics*10 (2021)We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms and, in addition, allows for a systematic expansion of the spin operators that respects the spin commutation relations within a truncated part of the full Hilbert space. Furthermore, the Newton series expansion strongly facilitates the calculation of expectation values with respect to coherent states. As a third example, we show that factorial moments and factorial cumulants arising in the context of photon or electron counting are a natural consequence of Newton series expansions. Finally, we elucidate the connection between normal ordering, Taylor and Newton series by determining a corresponding integral transformation, which is related to the Mellin transform. © 2021 SciPost Foundation. All right reserved.view abstract 10.21468/SCIPOSTPHYS.10.1.007 **Statistical analysis of spin switching in coupled spin-crossover molecules**

Stegmann, P. and Gee, A. and Kemp, N.T. and König, J.*Physical Review B*104 (2021)We study the switching behavior of two spin-crossover molecules residing in a nanojunction device consisting of two closely spaced gold electrodes. The spin states are monitored through a real-time measurement of the resistance of the junction. A statistical analysis of the resistance values, the occupation probabilities, and the lifetimes of the respective spin states shows that the two spin-crossover molecules are coupled to each other. We extract the parameters for a minimal model describing the two coupled spin-crossover molecules. Finally, we use the time dependence of factorial cumulants to study the impact of interactions between the two spin-crossover molecules on the switching dynamics. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.104.125431 **Synchronized coherent charge oscillations in coupled double quantum dots**

Kleinherbers, E. and Stegmann, P. and König, J.*Physical Review B*104 (2021)We study coherent charge oscillations in double quantum dots tunnel coupled to metallic leads. If two such systems are coupled by Coulomb interaction, there are, in total, six (instead of only two) oscillation modes of the entangled system with interaction-dependent oscillation frequencies. By tuning the bias voltage, one can engineer decoherence such that only one of the six modes, in which the charge oscillations in both double quantum dots become synchronized in antiphase, is singled out. We suggest using waiting-time distributions and the -correlation function to detect the common frequency and the phase locking. © 2021 American Physical Societyview abstract 10.1103/PhysRevB.104.165304 **Interaction-induced current asymmetries in resonant transport through interacting quantum-dot spin valves revealed by iterative summation of path integrals**

Mundinar, S. and Hucht, A. and König, J. and Weiss, S.*Physical Review B*102 (2020)Resonant tunneling of electrons between two ferromagnets and a quantum dot in the presence of an externally applied magnetic field reveals a strong gate dependence in the linear and nonlinear bias regime. This gate dependence originates from the interplay between Coulomb interactions and spin-dependent hybridization between the quantum dot and the leads. To take into account Coulomb interaction strengths of the same order of magnitude as the external magnetic field and the hybridization strength we adopt the numerically exact iterative summation of path integrals. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.045404 **Real-Time Detection of Single Auger Recombination Events in a Self-Assembled Quantum Dot**

Lochner, P. and Kurzmann, A. and Kerski, J. and Stegmann, P. and König, J. and Wieck, A.D. and Ludwig, Ar. and Lorke, A. and Geller, M.*Nano Letters*20 (2020)Auger recombination is a nonradiative process, where the recombination energy of an electron-hole pair is transferred to a third charge carrier. It is a common effect in colloidal quantum dots that quenches the radiative emission with an Auger recombination time below nanoseconds. In self-assembled QDs, the Auger recombination has been observed with a much longer recombination time on the order of microseconds. Here, we use two-color laser excitation on the exciton and trion transition in resonance fluorescence on a single self-assembled quantum dot to monitor in real-time single quantum events of the Auger process. Full counting statistics on the random telegraph signal give access to the cumulants and demonstrate the tunability of the Fano factor from a Poissonian to a sub-Poissonian distribution by Auger-mediated electron emission from the dot. Therefore, the Auger process can be used to tune optically the charge carrier occupation of the dot by the incident laser intensity, independently from the electron tunneling from the reservoir by the gate voltage. Our findings are not only highly relevant for the understanding of the Auger process but also demonstrate the perspective of the Auger effect for controlling precisely the charge state in a quantum system by optical means. © 2020 American Chemical Society.view abstract 10.1021/acs.nanolett.9b04650 **Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: Phenomenological description and its microscopic foundation**

Kleinherbers, E. and Szpak, N. and König, J. and Schützhold, R.*Physical Review B*101 (2020)We study relaxation dynamics in a strongly interacting two-site Fermi-Hubbard model that is induced by coupling each site to a local fermionic bath. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the time evolution of the reduced density matrix. In spite of a local coupling to the baths, the found Lindblad operators are nonlocal in space. We compare with the local approximation, where those nonlocal effects are neglected. Furthermore, we propose an improvement on the commonly used secular approximation (rotating-wave approximation), referred to as coherent approximation, which turns out superior in all studied parameter regimes (and equivalent otherwise). We look at the relaxation dynamics for several important observables and compare the methods for early and late times in various temperature regimes. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.101.125131 **Relaxation dynamics in double-spin systems**

Stegmann, P. and König, J. and Sothmann, B.*Physical Review B*101 (2020)We consider the relaxation dynamics of two spins coupled to a common bosonic bath. The time evolution is simulated by a generalized master equation derived within a real-time diagrammatic approach. Interference effects due to the coherent coupling to the common bath give rise to characteristic features in the relaxation dynamics after a quench or during a periodic external driving. In particular, we find that the long-time behavior during periodic driving depends sensitively on the initial state as well as on system parameters such as coupling asymmetries. When coupled to more than a single reservoir, the interference effects can lead to a cooling mechanism for one of the bosonic reservoirs. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.101.075411 **Iterative path-integral summations for the tunneling magnetoresistance in interacting quantum-dot spin valves**

Mundinar, S. and Stegmann, P. and König, J. and Weiss, S.*Physical Review B*99 (2019)We report on the importance of resonant-tunneling processes on quantum transport through interacting quantum-dot spin valves. To include Coulomb interaction in the calculation of the tunneling magnetoresistance (TMR), we reformulate and generalize the recently developed, numerically exact method of iterative summation of path integrals (ISPI) to account for spin-dependent tunneling. The ISPI scheme allows us to investigate weak to intermediate Coulomb interaction in a wide range of gate and bias voltage and down to temperatures at which a perturbative treatment of tunneling severely fails. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.99.195457 **Optical Detection of Single-Electron Tunneling into a Semiconductor Quantum Dot**

Kurzmann, A. and Stegmann, P. and Kerski, J. and Schott, R. and Ludwig, Ar. and Wieck, A.D. and König, J. and Lorke, A. and Geller, M.*Physical Review Letters*122 (2019)The maximum information of a dynamic quantum system is given by real-time detection of every quantum event, where the ultimate challenge is a stable, sensitive detector with high bandwidth. All physical information can then be drawn from a statistical analysis of the time traces. We demonstrate here an optical detection scheme based on the time-resolved resonance fluorescence on a single quantum dot. Single-electron resolution with high signal-to-noise ratio (4σ confidence) and high bandwidth of 10 kHz make it possible to record the individual quantum events of the transport dynamics. Full counting statistics with factorial cumulants gives access to the nonequilibrium dynamics of spin relaxation of a singly charged dot (γ↑↓=3 ms-1), even in an equilibrium transport measurement. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.122.247403 **Coherent dynamics in stochastic systems revealed by full counting statistics**

Stegmann, P. and König, J. and Weiss, S.*Physical Review B*98 (2018)Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.035409 **Revealing attractive electron-electron interaction in a quantum dot by full counting statistics**

Kleinherbers, E. and Stegmann, P. and König, J.*New Journal of Physics*20 (2018)Recent experiments (2015 Nature 521 196; 2017 Nat. Commun. 8 395) have presented evidence for electron pairing in a quantum dot beyond the superconducting regime. Here, we show that the impact of an attractive electron-electron interaction on the full counting statistics of electron transfer through a quantum dot is qualitatively different from the case of a repulsive interaction. In particular, the sign of higher-order (generalized) factorial cumulants reveals more pronounced correlations, which even survive in the limit of fast spin relaxation. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aad14a **Inverse counting statistics based on generalized factorial cumulants**

Stegmann, P. and König, J.*New Journal of Physics*19 (2017)We propose a procedure to reconstruct characteristic features of an unknown stochastic system from the long-time full counting statistics of some of the system's transitions that are monitored by a detector. The full counting statistics is conveniently parametrized by so-called generalized factorial cumulants. Taking only a few of them as input information is sufficient to reconstruct important features such as the lower bound of the system dimension and the full spectrum of relaxation rates. The use of generalized factorial cumulants reveals system dimensions and rates that are hidden for ordinary cumulants. We illustrate the inverse counting-statistics procedure for two model systems: a single-level quantum dot in a Zeeman field and a single-electron box subjected to sequential and Andreev tunneling. © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aa5a70 **Odd-triplet superconductivity in single-level quantum dots**

Weiss, S. and König, J.*Physical Review B*96 (2017)We study the interplay of spin and charge coherence in a single-level quantum dot. A tunnel coupling to a superconducting lead induces superconducting correlations in the dot. With full spin symmetry retained, only even-singlet superconducting correlations are generated. An applied magnetic field or attached ferromagnetic leads partially or fully reduce the spin symmetry, and odd-triplet superconducting correlations are generated as well. For single-level quantum dots, no other superconducting correlations are possible. We analyze, with the help of a diagrammatic real-time technique, the interplay of spin symmetry and superconductivity and its signatures in electronic transport, in particular current and shot noise. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.064529 **Thermal Conductance of a Single-Electron Transistor**

Dutta, B. and Peltonen, J.T. and Antonenko, D.S. and Meschke, M. and Skvortsov, M.A. and Kubala, B. and König, J. and Winkelmann, C.B. and Courtois, H. and Pekola, J.P.*Physical Review Letters*119 (2017)We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With a large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures. © 2017 American Physical Society.view abstract 10.1103/PhysRevLett.119.077701 **Violation of detailed balance for charge-transfer statistics in Coulomb-blockade systems**

Stegmann, P. and König, J.*Physica Status Solidi (B) Basic Research*254 (2017)We discuss the possibility to generate in Coulomb-blockade systems steady states that violate detailed balance. This includes both voltage biased and non-biased scenarios. The violation of detailed balance yields that the charge-transfer statistics for electrons tunneling into an island experiencing strong Coulomb interaction is different from the statistics for tunneling out. This can be experimentally tested by time-resolved measurement of the island's charge state. We demonstrate this claim for two model systems. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.view abstract 10.1002/pssb.201600507 **Short-time counting statistics of charge transfer in Coulomb-blockade systems**

Stegmann, P. and König, J.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)We study full counting statistics of electron tunneling in Coulomb-blockade systems in the limit of short measuring-time intervals. This limit is particularly suited to identify correlations among tunneling events, but only when analyzing the charge-transfer statistics in terms of factorial cumulants CF,m(t) rather than ordinary ones commonly used in literature. In the absence of correlations, the short-time behavior of the factorial cumulants is given by CF,m(t) (-1)m-1tm. A different sign and/or a different power law of the time dependence indicates correlations. We illustrate this for sequential and Andreev tunneling in a metallic single-electron box. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.125433 **Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium**

Stegmann, P. and Sothmann, B. and Hucht, A. and König, J.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)We introduce time-dependent, generalized factorial cumulants Csm(t) of the full counting statistics of electron transfer as a tool to detect interactions in nanostructures. The violation of the sign criterion (-1)m-1Csm(t)≥0 for any time t, order m, and parameter s proves the presence of interactions. For given system parameters, there is a minimal time span tmin and a minimal order m to observe the violation of the sign criterion. We demonstrate that generalized factorial cumulants are more sensitive to interactions than ordinary ones and can detect interactions even in regimes where ordinary factorial cumulants fail. We illustrate our findings with the example of a quantum dot tunnel coupled to electronic reservoirs either in or out of equilibrium. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.155413 **Determining energy relaxation length scales in two-dimensional electron gases**

Billiald, J. and Backes, D. and König, J. and Farrer, I. and Ritchie, D. and Narayan, V.*Applied Physics Letters*107 (2015)We present measurements of the energy relaxation length scale in two-dimensional electron gases (2DEG5). A temperature gradient is established in the 2DEG by means of a heating current, and then the elevated electron temperature T-e is estimated by measuring the resultant thermovoltage signal across a pair of deferentially biased bar-gates. We adapt a model by Rojek and König [Phys. Rev. B 90, 115403 (2014)] to analyse the thermovoltage signal and as a result extract l, T-e, and the power-law exponent alpha(i) for inelastic scattering events in the 2DEG. We show that in high-mobility 2DEGs, l can attain macroscopic values of several hundred microns, but decreases rapidly as the carrier density n is decreased. Our work demonstrates a versatile low-temperature thermometry scheme, and the results provide important insights into heat transport mechanisms in low-dimensional systems and nanostructures. These insights will be vital for practical design considerations of future nanoelectronic circuits. (C) 2015 AIP Publishing LLC.view abstract 10.1063/1.4926338 **Spin resonance without spin splitting**

Hell, M. and Sothmann, B. and Leijnse, M. and Wegewijs, M.R. and König, J.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)We predict that a single-level quantum dot without discernible splitting of its spin states develops a spin-precession resonance in charge transport when embedded into a spin valve. The resonance occurs in the generic situation of Coulomb blockaded transport with ferromagnetic leads whose polarizations deviate from perfect antiparallel alignment. The resonance appears when electrically tuning the interaction-induced exchange field perpendicular to one of the polarizations - a simple condition relying on vectors in contrast to usual resonance conditions associated with energy splittings. The spin resonance can be detected by stationary dI/dV spectroscopy and by oscillations in the time-averaged current using a gate-pulsing scheme. The generic noncollinearity of the ferromagnets and junction asymmetry allow for an all-electric determination of the spin-injection asymmetry, the anisotropy of spin relaxation, and the magnitude of the exchange field. We also investigate the impact of a nearby superconductor on the resonance position. Our simplistic model turns out to be generic for a broad class of coherent few-level quantum systems. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.195404 **Asymmetry of charge relaxation times in quantum dots: The influence of degeneracy**

Beckel, A. and Kurzmann, A. and Geller, M. P. and Ludwig, Ar. and Wieck, A.D. and König, J. and Lorke, A.*EPL*106 (2014)Using time-resolved transconductance spectroscopy, we study the tunneling dynamics between a two-dimensional electron gas (2DEG) and self-assembled quantum dots (QDs), embedded in a field-effect transistor structure. We find that the tunneling of electrons from the 2DEG into the QDs is governed by a different time constant than the reverse process, i.e., tunneling from the QDs to the 2DEG. This asymmetry is a clear signature of Coulomb interaction and makes it possible to determine the degeneracy of the quantum-dot orbitals even when the individual states cannot be resolved energetically because of inhomogeneous broadening. Our experimental data can be qualitatively explained within a master-equation approach. © CopyrightEPLA, 2014.view abstract 10.1209/0295-5075/106/47002 **Mesoscopic diffusion thermopower in two-dimensional electron gases**

Rojek, S. and König, J.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)The diffusion of energy that is locally deposited into two-dimensional electron gases by Joule heating generates transverse voltages across devices with broken symmetry. For mesoscopic structures characterized by device dimensions comparable to the energy diffusion length, the resulting thermopower strongly depends on details of the potential profile defined by electric gates. We discuss these mesoscopic features within a diffusion thermopower model and propose schemes to measure the energy diffusion length and its dependence on gate voltage. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.115403 **Spin pumping through quantum dots**

Rojek, S. and Governale, M. and König, J.*Physica Status Solidi (B) Basic Research*251 (2014)We propose schemes for generating spin currents into a semiconductor by adiabatic or non-adiabatic pumping of electrons through interacting quantum dots. The appeal of such schemes lies in the possibility to tune the pumping characteristics via gate voltages that control the properties of the quantum dot. The calculations are based on a systematic perturbation expansion in the tunnel-coupling strength and the pumping frequency, expressed within a diagrammatic real-time technique. Special focus is put on the possibility of pure spin pumping, i.e., of pumping spin currents without charge currents. Setup of a device for generating a spin current into a semiconductor by adiabatic or non-adiabatic pumping of electrons through an interacting quantum dot. © 2014 The Authors. Phys. Status Solidi B is published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.view abstract 10.1002/pssb.201350213 **Unconventional superconductivity in double quantum dots**

Sothmann, B. and Weiss, S. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)The formation of electron pairs is a prerequisite of superconductivity. The fermionic nature of electrons yields four classes of superconducting correlations with definite symmetry in spin, space, and time. Here, we suggest double quantum dots coupled to conventional s-wave superconductors in the presence of inhomogeneous magnetic fields as a model system exhibiting unconventional pairing. Due to their small number of degrees of freedom, tunable by gate voltages, quantum-dot systems are ideal to gain fundamental insight into unconventional pairing. We propose two detection schemes for unconventional superconductivity, based on either Josephson or Andreev spectroscopy. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.220501 **Adiabatic pumping through an interacting quantum dot with spin-orbit coupling**

Rojek, S. and König, J. and Shnirman, A.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We study adiabatic pumping through a two-level quantum dot with spin-orbit coupling. Using a diagrammatic real-time approach, we calculate both the pumped charge and spin for a periodic variation of the dot's energy levels in the limit of weak tunnel coupling. Thereby, we compare the two limits of vanishing and infinitely large charging energy on the quantum dot. We discuss the dependence of the pumped charge and pumped spin on gate voltages, the symmetry in the tunnel-matrix elements, and spin-orbit coupling strength. We identify the possibility to generate pure spin currents in the absence of charge currents. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.075305 **Josephson-Majorana cycle in topological single-electron hybrid transistors**

Didier, N. and Gibertini, M. and Moghaddam, A.G. and König, J. and Fazio, R.*Physical Review B - Condensed Matter and Materials Physics*88 (2013)Charge transport through a small topological superconducting island in contact with a normal and a superconducting electrode occurs through a cycle that involves coherent oscillations of Cooper pairs and tunneling in/out the normal electrode through a Majorana bound state, the Josephson-Majorana cycle. We illustrate this mechanism by studying the current-voltage characteristics of a superconductor-topological superconductor-normal metal single-electron transistor. At low bias and temperature the Josephson-Majorana cycle is the dominant mechanism for transport. We discuss a three-terminal configuration where the nonlocal character of the Majorana bound states is emergent. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.88.024512 **Renormalization effects in interacting quantum dots coupled to superconducting leads**

Futterer, D. and Swiebodzinski, J. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We study subgap transport through an interacting quantum dot tunnel coupled to one normal and two superconducting leads. To check the reliability of an approximation of an infinitely large gap Δ in the superconducting leads and weak tunnel coupling to the normal lead, we perform a 1/Δ expansion, and we analyze next-to-leading-order corrections in the tunnel coupling to the normal lead. Furthermore, we propose a resummation approach to calculate the Andreev bound states for finite Δ. The results are substantially more accurate than those obtained by mean-field treatments and favorably compare with numerical exact results. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.014509 **Theory of spin pumping through an interacting quantum dot tunnel coupled to a ferromagnet with time-dependent magnetization**

Winkler, N. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We investigate two schemes for pumping spin adiabatically from a ferromagnet through an interacting quantum dot into a normal lead that exploit the possibility to vary in time the ferromagnet's magnetization, either its amplitude or its direction. For this purpose, we extend a diagrammatic real-time technique for pumping to situations in which the leads' properties are time dependent. In the first scheme, the time-dependent magnetization amplitude is combined with a time-dependent level position of the quantum dot to establish both a charge and a spin current. The second scheme uses a uniform rotation of the ferromagnet's magnetization direction to generate a pure spin current without a charge current. We discuss the influence of an interaction-induced exchange field on the pumping characteristics. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.155428 **Zero-frequency noise in adiabatically driven interacting quantum systems**

Riwar, R.-P. and Splettstoesser, J. and König, J.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We investigate current-current correlations of adiabatic charge pumping through interacting quantum dots weakly coupled to reservoirs. To calculate the zero-frequency noise for a time-dependently driven system, possibly in the presence of an additional dc bias, we perform within a real-time diagrammatic approach a perturbative expansion in the tunnel coupling to the reservoirs in leading and next-to-leading orders. We apply this formalism to study the adiabatic correction to the zero-frequency noise, i.e., the pumping noise, in the case of a single-level quantum dot charge pump. If no stationary bias is applied, the adiabatic correction shows Coulomb-interaction-induced deviations from the fluctuation-dissipation theorem. Furthermore, we show that the adiabatic correction to the Fano factor carries information about the coupling asymmetry and is independent of the choice of the pumping parameters. When including a time-dependent finite bias, we find that there can be pumping noise even if there is zero adiabatically pumped charge. The pumping noise also indicates the respective direction of the bias-induced current and the pumping current. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.195407 **Ac Josephson transport through interacting quantum dots**

Hiltscher, B. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)We investigate the ac Josephson current through a quantum dot with strong Coulomb interaction attached to two superconducting and one normal lead. To this end, we perform a perturbation expansion in the tunneling couplings within a diagrammatic real-time technique. The ac Josephson current is connected to the reduced density matrix elements that describe superconducting correlations induced on the quantum dot via proximity effect. We analyze the dependence of the ac signal on the level position of the quantum dot, the charging energy, and the applied bias voltages. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.235427 **Current fluctuations in noncollinear single-electron spin-valve transistors**

Lindebaum, S. and König, J.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)We present a theoretical framework to analyze fluctuations of electric current through a noncollinear single-electron spin-valve transistor in the limit of weak tunnel coupling. The system under consideration consists of two tunnel junctions that connect a small, nonmagnetic metallic island to two ferromagnetic leads with noncollinear magnetization. We study the current noise spectrum as a function of bias voltage, frequency, and the relative angle between the leads' magnetization directions and find that both the zero- and the finite-frequency current noise are strongly affected by charging energy and spin accumulation in the island. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.125306 **Driven superconducting proximity effect in interacting quantum dots**

Moghaddam, A.G. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)We present a theory of nonequilibrium superconducting proximity effect in an interacting quantum dot induced by a time-dependent tunnel coupling between the dot and a superconducting lead. The proximity effect, which is established when the driving frequency fulfills a gate-voltage-dependent resonance condition, can be probed through the tunneling current into a weakly coupled normal lead. Furthermore, we propose to generate and manipulate coherent superpositions of quantum-dot states with electron numbers differing by two by applying pulsed oscillatory variations to the couplings between the dot and superconductors. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.094518 **Mesoscopic stoner instability in metallic nanoparticles revealed by shot noise**

Sothmann, B. and König, J. and Gefen, Y.*Physical Review Letters*108 (2012)We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallel magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe the mesoscopic Stoner instability. © 2012 American Physical Society.view abstract 10.1103/PhysRevLett.108.166603 **Time scales in the dynamics of an interacting quantum dot**

Contreras-Pulido, L.D. and Splettstoesser, J. and Governale, M. and König, J. and Büttiker, M.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)We analyze the dynamics of a single-level quantum dot with Coulomb interaction, weakly tunnel coupled to an electronic reservoir, after it has been brought out of equilibrium, e.g., by a step-pulse potential. We investigate the exponential decay toward the equilibrium state, which is governed by three time scales. In addition to the charge and spin relaxation time there is a third time scale which is independent of the level position and the Coulomb interaction. This time scale emerges in the time evolution of physical quantities sensitive to two-particle processes. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.075301 **Transverse rectification in density-modulated two-dimensional electron gases**

Ganczarczyk, A. and Rojek, S. and Quindeau, A. and Geller, M. P. and Hucht, A. and Notthoff, C. and König, J. and Lorke, A. and Reuter, D. and Wieck, A.D.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)We demonstrate tunable transverse rectification in a density-modulated two-dimensional electron gas (2DEG). The density modulation is induced by two surface gates, running in parallel along a narrow stripe of 2DEG. A transverse voltage in the direction of the density modulation is observed, i.e., perpendicular to the applied source-drain voltage. The polarity of the transverse voltage is independent of the polarity of the source-drain voltage, demonstrating rectification in the device. We find that the transverse voltage U y depends quadratically on the applied source-drain voltage and nonmonotonically on the density modulation. The experimental results are discussed in the framework of a diffusion thermopower model. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.085309 **Tunneling-induced renormalization in interacting quantum dots**

Splettstoesser, J. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)We analyze tunneling-induced quantum fluctuations in a single-level quantum dot with arbitrarily strong on-site Coulomb interaction, generating cotunneling processes and renormalizing system parameters. For a perturbative analysis of these quantum fluctuations, we remove off-shell parts of the Hamiltonian via a canonical transformation. We find that the tunnel couplings for the transitions connecting empty and single occupation and connecting single and double occupation of the dot renormalize with the same magnitude but with opposite signs. This has an important impact on the shape of the renormalization extracted, for example, from the conductance. Finally, we verify the compatibility of our results with a systematic second-order perturbation expansion of the linear conductance performed within a diagrammatic real-time approach. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.035432 **Adiabatic pumping in a double-dot Cooper-pair beam splitter**

Hiltscher, B. and Governale, M. and Splettstoesser, J. and König, J.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We study adiabatic pumping through a double quantum dot coupled to normal and superconducting leads. For this purpose a perturbation expansion in the tunnel coupling between the dots and the normal leads is performed and processes underlying the pumping current are discussed. Features of crossed Andreev reflection are investigated in the average pumped charge and related to local Andreev reflection in a single quantum dot. In order to distinguish Cooper-pair splitting from quasiparticle pumping, we compare the properties of Cooper-pair pumping with single-electron pumping in a system with only normal leads. The dependence on the average dot level and the coupling asymmetry turn out to be the main distinguishing features. This is contrasted with the linear conductance for which it is more difficult to distinguish single-particle from Cooper-pair transport. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.155403 **Band-mixing-mediated Andreev reflection of semiconductor holes**

Futterer, D. and Governale, M. and Zülicke, U. and König, J.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We have investigated Andreev-reflection processes occurring at a clean interface between a p-type semiconductor and a conventional superconductor. Our calculations are performed within a generalized Bogoliubov-de Gennes formalism where the details of the semiconductor band structure are described by a 6×6 Kane model. It is found that Andreev reflection of light-hole and heavy-hole valence-band carriers is generally possible and that the two valence-band hole types can be converted into each other in the process. The normal-reflection and Andreev-reflection amplitudes depend strongly on the semiconductor's carrier concentration and on the angle of injection. In the special case of perpendicular incidence, Andreev reflection of heavy holes does not occur. Moreover, we find conversionless Andreev reflection to be impossible above some critical angle, and another critical angle exists above which the conversion of a heavy hole into a light hole cannot occur. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.104526 **Effect of increased charring on the narrow side of rectangular timber cross-sections exposed to fire on three or four sides**

Frangi, A. and König, J.*Fire and Materials*35 (2011)Owing to the influence of two-dimensional heat transfer, fire tests and heat transfer calculations show that charring on the narrow side of rectangular timber cross-sections may be considerably greater than charring on the wide side. For timber members unprotected throughout the time of fire exposure as well as members initially protected from fire exposure, it is shown by calculation, that the relationship between charring on the narrow side and time is nonlinear. In order to take into account increased charring on the narrow side of timber members a section factor ks was determined. By calculation it is shown that bending moment resistance is only insignificantly influenced by the effect of two-dimensional heat transfer and the factor k s can therefore be neglected, making the fire design of timber members easier. © 2011 John Wiley & Sons, Ltd.view abstract 10.1002/fam.1078 **Manipulating single spins in quantum dots coupled to ferromagnetic leads**

König, J. and Braun, M. and Martinek, J.*Lecture Notes in Physics*820 (2011)view abstract 10.1007/978-3-642-14376-2_6 **Superconducting proximity effect in interacting quantum dots revealed by shot noise**

Braggio, A. and Governale, M. and Pala, M. G. and König, J.*Solid State Communications*151 (2011)We study the full counting statistics of charge transport through a quantum dot tunnel coupled to one normal and one superconducting lead with a large superconducting gap. As a function of the level detuning, there is a crossover from a regime with strong superconducting correlations in the quantum dot to a regime in which the proximity effect on the quantum dot is suppressed. We analyze the current fluctuations of this crossover in the shot-noise regime. In particular, we predict that the full counting statistics changes from Poissonian with charge 2e, typical for Cooper pairs, to Poissonian with charge e, When the superconducting proximity effect is present. Thus, the onset of the superconducting proximity effect is revealed by the reduction of the Fano factor from 2 to 1. (C) 2010 Elsevier Ltd. All rights reserved.view abstract 10.1016/j.ssc.2010.10.043 **Theory of transport through noncollinear single-electron spin-valve transistors**

Lindebaum, S. and König, J.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We study the electronic transport through a noncollinear single-electron spin-valve transistor. It consists of a small metallic island weakly coupled to two ferromagnetic leads with noncollinear magnetization directions. The electric current is influenced by Coulomb charging and by spin accumulation. Furthermore, the interplay of Coulomb interaction and tunnel coupling to spin-polarized leads yields a many-body exchange field in which the accumulated island spin precesses. We analyze the effects of this exchange field in both the linear and nonlinear transport regime. In particular, we find that the exchange field can give rise to a high sensitivity of the island's spin orientation on the gate voltage. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.235409 **Charge and spin dynamics in interacting quantum dots**

Splettstoesser, J. and Governale, M. and König, J. and Büttiker, M.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)The transient response of a quantum dot with strong Coulomb interaction to a fast change in the gate potential, as well as the stationary ac response to a slow harmonic variation in the gate potential are computed by means of a real-time diagrammatic expansion in the tunnel-coupling strength. We find that after a fast switching, the exponential relaxation behavior of charge and spin are governed by a single time constant each, which differ from each other due to Coulomb repulsion. We compare the response to a step potential with the RC time extracted from the ac response. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.165318 **Generation of pure spin currents by superconducting proximity effect in quantum dots**

Futterer, D. and Governale, M. and König, J.*EPL*91 (2010)We investigate electronic transport in a three-terminal hybrid system, composed by an interacting quantum dot tunnel coupled to one superconducting, one ferromagnetic, and one normal lead. Despite the tendency of the charging energy to suppress the superconducting proximity effect when the quantum dot is in equilibrium, the non-equilibrium proximity effect can give rise to a large Andreev current. The presence of the ferromagnet can lead to a finite spin accumulation on the dot. We find that the interplay of the Andreev current and spin accumulation can generate a pure spin current, with no associated charge transport, in the normal lead. This situation is realised by tuning the quantum-dot spectrum by means of a gate voltage. Copyright © 2010 EPLA.view abstract 10.1209/0295-5075/91/47004 **Influence of spin waves on transport through a quantum-dot spin valve**

Sothmann, B. and König, J. and Kadigrobov, A.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We study the influence of spin waves on transport through a single-level quantum dot weakly coupled to ferromagnetic electrodes with noncollinear magnetizations. Side peaks appear in the differential conductance due to emission and absorption of spin waves. We, furthermore, investigate the nonequilibrium magnon distributions generated in the source and drain lead. In addition, we show how magnon-assisted tunneling can generate a fully spin-polarized current without an applied transport voltage. We discuss the influence of spin waves on the current noise. Finally, we show how the magnonic contributions to the exchange field can be detected in the finite-frequency Fano factor. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.205314 **Interference and interaction effects in adiabatic pumping through quantum dots**

Hiltscher, B. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)In order to investigate the effects of interference and interaction in adiabatic pumping, we consider an Aharonov-Bohm (AB) interferometer with a quantum dot embedded either in one or in both arms. We employ a real-time formalism and we perform an expansion both in the tunnel-coupling strengths between dot and leads and in the pumping frequency, taking into account the Coulomb interaction nonperturbatively. We find that pumping in a single-dot AB interferometer has a peristaltic but phase-coherent character. In a double-dot AB interferometer, we find a pumping mechanism that relies purely on quantum-mechanical interference and has no classical counterpart. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.085302 **Nonequilibrium current and noise in inelastic tunneling through a magnetic atom**

Sothmann, B. and König, J.*New Journal of Physics*12 (2010)In a recent experiment, Hirjibehedin et al (2007 Science 317 1199) performed inelastic tunneling spectroscopy of a single iron atom absorbed on a nonmagnetic substrate. The observed steps in the differential conductance marked the spin excitation energies. In this paper, we explain the observed nonmonotonicities in the differential conductance by a nonequilibrium population of the atom spin states. Furthermore, we predict super-Poissonian current noise due to this nonequilibrium situation. We argue that the remarkable absence of nonequilibrium features at certain conductance steps indicates the presence of an anisotropic relaxation channel. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/12/8/083028 **Probing the exchange field of a quantum-dot spin valve by a superconducting lead**

Sothmann, B. and Futterer, D. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)Electrons in a quantum-dot spin valve, consisting of a single-level quantum dot coupled to two ferromagnetic leads with magnetizations pointing in arbitrary directions, experience an exchange field that is induced on the dot by the interplay of Coulomb interaction and quantum fluctuations. We show that a third, superconducting lead with large superconducting gap attached to the dot probes this exchange field very sensitively. In particular, we find striking signatures of the exchange field in the symmetric component of the supercurrent with respect to the bias voltage applied between the ferromagnets already for small values of the ferromagnets' spin polarization. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.094514 **Spin-dependent transport through quantum-dot aharonov-bohm interferometers**

Hiltscher, B. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We study the influence of spin polarization on the degree of coherence of electron transport through interacting quantum dots. To this end, we identify transport regimes in which the degree of coherence can be related to the visibility of the Aharonov-Bohm oscillations in the current through a quantum-dot Aharonov-Bohm interferometer with one normal and one ferromagnetic lead. For these regimes, we calculate the visibility and, thus, the degree of coherence, as a function of the degree of spin polarization of the ferromagnetic lead. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.165452 **Superconducting proximity effect in interacting double-dot systems**

Eldridge, J. and Pala, M.G. and Governale, M. and König, J.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We study subgap transport from a superconductor through a double quantum dot with large on-site Coulomb repulsion to two normal leads. Nonlocal superconducting correlations in the double dot are induced by the proximity to the superconducting lead, detectable in nonlocal Andreev transport that splits Cooper pairs in locally separated, spin-entangled electrons. We find that the I-V characteristics are strongly asymmetric: for a large bias voltage of certain polarity, transport is blocked by populating the double dot with states whose spin symmetry is incompatible with the superconductor. Furthermore, by tuning gate voltages one has access to splitting of the Andreev excitation energies, which is visible in the differential conductance. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.184507 **Transport through quantum-dot spin valves containing magnetic impurities**

Sothmann, B. and König, J.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We investigate transport through a single-level quantum dot coupled to noncollinearly magnetized ferromagnets in the presence of localized spins in either the tunnel barrier or on the quantum dot. For a large, anisotropic spin embedded in the tunnel barrier, our main focus is on the impurity excitations and the current-induced switching of the impurity that lead to characteristic features in the current. In particular, we show how the Coulomb interaction on the quantum dot can provide more information from tunnel spectroscopy of the impurity spin. In the case of a small spin on the quantum dot, we find that the frequency-dependent Fano factor can be used to study the nontrivial, coherent dynamics of the spins on the dot due to the interplay between exchange interaction and coupling to external and exchange magnetic fields. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.245319

#### charge and spin pumping

#### diagrammatic transport theory

#### many-particle systems

#### nanostructures

#### quantum dots

#### quantum transport

#### quantum-dot spin valves

#### spintronics

#### thermoelectrics

#### transport

#### tunnel magneto resistance