#### Prof. Dr. Björn Sothmann

Theoretical Physics

University of Duisburg-Essen

##### Contact

- bjoerns[at]thp[dot]uni-due[dot]de
- +49 0203 379 1578
- personal website

##### Hub

**Pair-amplitude dynamics in strongly coupled superconductor-quantum dot hybrids**

Heckschen, M. and Sothmann, B.*Physical Review B*105 (2022)We consider a three-terminal system consisting of a quantum dot strongly coupled to two superconducting reservoirs in the infinite-gap limit and weakly coupled to a normal metal. Using a real-time diagrammatic approach, we calculate the dynamics of the proximity-induced pair amplitude on the quantum dot. We find that after a quench the pair amplitude shows pronounced oscillations with a frequency determined by the coupling to the superconductors. In addition, it decays exponentially on a timescale set by the coupling to the normal metal. Strong oscillations of the pair amplitude occur also when the system is periodically driven both in the adiabatic and fast-driving limit. We relate the dynamics of the pair amplitude to the Josephson and Andreev current through the dot to demonstrate that it is an experimentally accessible quantity. © 2022 American Physical Society.view abstract 10.1103/PhysRevB.105.045420 **Ultrafast transport and energy relaxation of hot electrons in Au/Fe/MgO(001) heterostructures analyzed by linear time-resolved photoelectron spectroscopy**

Kühne, F. and Beyazit, Y. and Sothmann, B. and Jayabalan, J. and Diesing, D. and Zhou, P. and Bovensiepen, U.*Physical Review Research*4 (2022)view abstract 10.1103/PhysRevResearch.4.033239 **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 **Higgs-like pair amplitude dynamics in superconductor-quantum-dot hybrids**

Kamp, M. and Sothmann, B.*Physical Review B*103 (2021)We consider a quantum dot weakly tunnel coupled to superconducting reservoirs. A finite superconducting pair amplitude can be induced on the dot via the proximity effect. We investigate the dynamics of the induced pair amplitude after a quench and under periodic driving of the system by means of a real-time diagrammatic approach. We find that the quench dynamics is dominated by an exponential decay towards equilibrium. In contrast, the periodically driven system can sustain coherent oscillations of both the amplitude and the phase of the induced pair amplitude in analogy to Higgs and Nambu-Goldstone modes in driven bulk superconductors. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.103.045414 **Phase-dependent transport in thermally driven superconducting single-electron transistors**

Bauer, A.G. and Sothmann, B.*Physical Review B*104 (2021)We investigate thermally driven transport of heat and charge in a superconducting single-electron transistor by means of a real-time diagrammatic transport theory. Our theoretical approach allows us to account for strong Coulomb interactions and arbitrary nonequilibrium conditions while performing a systematic expansion in the tunnel coupling. We find that a temperature bias across the system gives rise to finite heat and charge currents close to the particle-hole symmetric point which depend both on the gate voltage as well as on the phase difference between the superconducting reservoirs. The finite thermoelectric effect arises due to level renormalization from virtual tunneling processes. Furthermore, we find that the phase bias can give rise to finite charge currents even in the presence of an inversion-symmetric temperature bias. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.104.195418 **Quantized phase-coherent heat transport of counterpropagating Majorana modes**

Bauer, A.G. and Scharf, B. and Molenkamp, L.W. and Hankiewicz, E.M. and Sothmann, B.*Physical Review B*104 (2021)We demonstrate that phase-coherent heat transport constitutes a powerful tool to probe Majorana physics in topological Josephson junctions. We predict that the thermal conductance transverse to the direction of the superconducting phase bias is universally quantized by half the thermal conductance quantum at phase difference φ=π. This is a direct consequence of the parity-protected counterpropagating Majorana modes which are hosted at the superconducting interfaces. Away from φ=π, we find a strong suppression of the thermal conductance due to the opening of a gap in the Andreev spectrum. This behavior is very robust with respect to the presence of magnetic fields. It is in direct contrast to the thermal conductance of a trivial Josephson junction which is suppressed at any phase difference φ. Thus, thermal transport can provide strong evidence for the existence of Majorana modes in topological Josephson junctions. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.104.L201410 **Phase-coherent caloritronics with ordinary and topological Josephson junctions**

Hwang, S.-Y. and Sothmann, B.*European Physical Journal: Special Topics*229 (2020)We provide a brief and comprehensive overview over recent developments in the field of phase-coherent caloritronics in ordinary and topological Josephson junctions. We start from the simple case of a short, one-dimensional superconductor-normal metal-superconductor (S-N-S) Josephson junction and derive the phase-dependent thermal conductance within the Bogoliubov-de Gennes formalism. Then, we review the key experimental breakthroughs that have triggered the recent growing interest into phase-coherent heat transport. They include the realization of thermal interferometers, diffractors, modulators and routers based on superconducting tunnel junctions. Finally, we discuss very recent theoretical findings based on superconductor-topological insulator-superconductor (S-TI-S) Josephson junctions that show interesting heat transport properties due to the interplay between topological band structures and superconductivity. © 2020, The Author(s).view abstract 10.1140/epjst/e2019-900094-y **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 **Thermally Induced Crossover from 2D to 1D Behavior in an Array of Atomic Wires: Silicon Dangling-Bond Solitons in Si(553)-Au**

Hafke, B. and Brand, C. and Witte, T. and Sothmann, B. and Horn-von Hoegen, M. and Erwin, S.C.*Physical Review Letters*124 (2020)The self-assembly of submonolayer amounts of Au on the densely stepped Si(553) surface creates an array of closely spaced "atomic wires" separated by 1.5 nm. At low temperature, charge transfer between the terraces and the row of silicon dangling bonds at the step edges leads to a charge-ordered state within the row of dangling bonds with ×3 periodicity. Interactions between the dangling bonds lead to their ordering into a fully two-dimensional (2D) array with centered registry between adjacent steps. We show that as the temperature is raised, soliton defects are created within each step edge. The concentration of solitons rises with increasing temperature and eventually destroys the 2D order by decoupling the step edges, reducing the effective dimensionality of the system to 1D. This crossover from higher to lower dimensionality is unexpected and, indeed, opposite to the behavior in other systems. © 2020 American Physical Society.view abstract 10.1103/PhysRevLett.124.016102 **Experimental realization of a quantum dot energy harvester**

Jaliel, G. and Puddy, R.K. and Sánchez, R. and Jordan, A.N. and Sothmann, B. and Farrer, I. and Griffiths, J.P. and Ritchie, D.A. and Smith, C.G.*Physical Review Letters*123 (2019)We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He3/He4 dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.123.117701 **Nonlinear chiral refrigerators**

Sánchez, D. and Sánchez, R. and López, R. and Sothmann, B.*Physical Review B*99 (2019)We investigate a mesoscopic refrigerator based on chiral quantum Hall edge channels. We discuss a three-terminal cooling device in which charge transport occurs only between a pair of voltage-biased terminals. The third terminal, which is to be cooled, is set as a voltage probe with vanishing particle flux. This largely prevents the generation of direct Joule heating, which ensures a high coefficient of performance. Cooling operation is based on energy-dependent quantum transmissions. The latter are implemented with the aid of two tunable scattering resonances (quantum dots). To find the optimal performance point and the largest temperature difference created with our refrigerator, it is crucial to address the nonlinear regime of transport, accounting for electron-electron interaction effects. Our numerical simulations show that the maximal cooling power can be tuned with the quantum dot couplings and energy levels. Further, we provide analytical expressions within a weakly nonlinear scattering-matrix formalism which allow us to discuss the conditions for optimal cooling in terms of generalized thermopowers. Our results are important for the assessment of chiral conductors as promising candidates for efficient quantum refrigerators with low dissipation. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.99.245304 **Phase-dependent heat and charge transport through superconductor-quantum dot hybrids**

Kamp, M. and Sothmann, B.*Physical Review B*99 (2019)We analyze heat and charge transport through a single-level quantum dot coupled to two BCS superconductors at different temperatures to first order in the tunnel coupling. In order to describe the system theoretically, we extend a real-time diagrammatic technique that allows us to capture the interplay between superconducting correlations, strong Coulomb interactions, and nonequilibrium physics. We find that a thermoelectric effect can arise due to the superconducting proximity effect on the dot. In the nonlinear regime, the thermoelectric current can also flow at the particle-hole symmetric point due to a level renormalization caused by virtual tunneling between the dot and the leads. The heat current through the quantum dot is sensitive to the superconducting phase difference. In the nonlinear regime, the system can act as a thermal diode. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.99.045428 **Phase-dependent heat transport in Josephson junctions with p -wave superconductors and superfluids**

Bauer, A.G. and Sothmann, B.*Physical Review B*99 (2019)We investigate phase-coherent thermal transport in Josephson junctions made from unconventional superconductors or superfluids. The thermal conductance is evaluated for one- and two-dimensional junctions within the Bogoliubov-de Gennes formalism. We analyze three different scenarios of junctions between two triplet superconductors with (i) helical pairing, (ii) unitary chiral pairing, and (iii) nonunitary chiral pairing. We find that the phase-dependent thermal conductance allows us to distinguish the different pairings and provides insight into the formation of topologically nontrivial Andreev bound states in the junction. ©2019 American Physical Society.view abstract 10.1103/PhysRevB.99.214508 **Phase-Tunable Thermal Rectification in the Topological SQUIPT**

Bours, L. and Sothmann, B. and Carrega, M. and Strambini, E. and Braggio, A. and Hankiewicz, E.M. and Molenkamp, L.W. and Giazotto, F.*Physical Review Applied*11 (2019)We theoretically explore the behavior of thermal transport in the topological SQUIPT, in the linear and nonlinear regime. The device consists of a topological Josephson junction based on a two-dimensional topological insulator in contact with two superconducting leads, and a probe tunnel coupled to the topological edge states of the junction. We compare the performance of a normal metal and a graphene probe, showing that the topological SQUIPT behaves as a passive thermal rectifier and that it can reach a rectification coefficient of up to 145% with the normal metal probe. Moreover, the interplay between the superconducting leads and the helical edge states leads to a unique behavior due to a Doppler-shift-like effect that allows one to influence quasiparticle transport through the edge channels via the magnetic flux that penetrates the junction. Exploiting this effect, we can greatly enhance the rectification coefficient for temperatures below the critical temperature TC in an active rectification scheme. © 2019 American Physical Society.view abstract 10.1103/PhysRevApplied.11.044073 **Thermal transistor and thermometer based on Coulomb-coupled conductors**

Yang, J. and Elouard, C. and Splettstoesser, J. and Sothmann, B. and Sánchez, R. and Jordan, A.N.*Physical Review B*100 (2019)We study a three-terminal setup consisting of a single-level quantum dot capacitively coupled to a quantum point contact. The point contact connects to a source and drain reservoir while the quantum dot is coupled to a single base reservoir. This setup has been used to implement a noninvasive, nanoscale thermometer for the bath reservoir by detecting the current in the quantum point contact. Here, we demonstrate that the device can also be operated as a thermal transistor where the average (charge and heat) current through the quantum point contact is controlled via the temperature of the base reservoir. We characterize the performances of this device both as a transistor and a thermometer and derive the operating condition maximizing their respective sensitivities. The present analysis is useful for the control of charge and heat flow and high precision thermometry at the nanoscale. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.100.045418 **Illumination-induced nonequilibrium charge states in self-assembled quantum dots**

Valentin, S.R. and Schwinger, J. and Eickelmann, P. and Labud, P.A. and Wieck, A.D. and Sothmann, B. and Ludwig, Ar.*Physical Review B*97 (2018)We report on capacitance-voltage spectroscopy of self-assembled InAs quantum dots under constant illumination. Besides the electronic and excitonic charging peaks in the spectrum reported earlier, we find additional resonances associated with nonequilibrium state tunneling unseen in C(V) measurements before. We derive a master-equation-based model to assign the corresponding quantum state tunneling to the observed peaks. C(V) spectroscopy in a magnetic field is used to verify the model-assigned nonequilibrium peaks. The model is able to quantitatively address various experimental findings in C(V) spectroscopy of quantum dots such as the frequency- and illumination-dependent peak height, a thermal shift of the tunneling resonances and the occurrence of the additional nonequilibrium peaks. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.045416 **Odd-frequency superconductivity revealed by thermopower**

Hwang, S.-Y. and Burset, P. and Sothmann, B.*Physical Review B*98 (2018)Superconductivity is characterized by a nonvanishing superconducting pair amplitude. It has a definite symmetry in spin, momentum, and frequency (time). While the spin and momentum symmetry have been probed experimentally for different classes of superconductivity, the odd-frequency nature of certain superconducting correlations has not been demonstrated yet in a direct way. Here, we propose the thermopower as an unambiguous way to assess odd-frequency superconductivity. This is possible since the thermoelectric coefficient given by Andreev-like processes is only finite in the presence of odd-frequency superconductivity. We illustrate our general findings with a simple example of a superconductor-quantum-dot-ferromagnet hybrid. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.161408 **Phase-Coherent Heat Circulator Based on Multiterminal Josephson Junctions**

Hwang, S.-Y. and Giazotto, F. and Sothmann, B.*Physical Review Applied*10 (2018)We theoretically propose a phase-coherent thermal circulator based on ballistic multiterminal Josephson junctions. The breaking of time-reversal symmetry by either a magnetic flux or a superconducting phase bias allows heat to flow preferentially in one direction from one terminal to the next while heat flow in the opposite direction is suppressed. We find that our device can achieve a high circulation efficiency over a wide range of parameters and that its performance is robust with respect to the presence of disorder. We provide estimates for the expected heat currents for realistic samples. © 2018 American Physical Society.view abstract 10.1103/PhysRevApplied.10.044062 **Topological SQUIPT Based on Helical Edge States in Proximity to Superconductors**

Bours, L. and Sothmann, B. and Carrega, M. and Strambini, E. and Hankiewicz, E.M. and Molenkamp, L.W. and Giazotto, F.*Physical Review Applied*10 (2018)We propose a device based on a topological Josephson junction where the helical edge states of a two-dimensional (2D) topological insulator are in close proximity to two superconducting leads. The presence of a magnetic flux through the junction leads to a Doppler shift in the spectrum of Andreev bound states, and affects the quantum interference between proximized edge states. We inspect the emergent features, accessing the density of states through a tunnel-coupled metallic probe, thus realizing a topological superconducting quantum-interference-proximity transistor (TSQUIPT). We calculate the expected performance of this device, concluding that it can be used as a sensitive absolute magnetometer due to the voltage drop across the junction decaying to a constant value as a function of the magnetic flux. Contrary to conventional SQUID and SQUIPT designs, no ring structure is needed. The findings pave the way for sensitive hybrid devices that exploit the helical edge states of a 2D topological insulator. © 2018 American Physical Society.view abstract 10.1103/PhysRevApplied.10.014027 **High-efficiency thermal switch based on topological Josephson junctions**

Sothmann, B. and Giazotto, F. and Hankiewicz, E.M.*New Journal of Physics*19 (2017)We propose theoretically a thermal switch operating by the magnetic-flux controlled diffraction of phase-coherent heat currents in a thermally biased Josephson junction based on a two-dimensional topological insulator. For short junctions, the system shows a sharp switching behavior while for long junctions the switching is smooth. Physically, the switching arises from the Doppler shift of the superconducting condensate due to screening currents induced by a magnetic flux. We suggest a possible experimental realization that exhibits a relative temperature change of 40% between the on and off state for realistic parameters. This is a factor of two larger than in recently realized thermal modulators based on conventional superconducting tunnel junctions. © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aa60d4 **Majorana STM as a perfect detector of odd-frequency superconductivity**

Kashuba, O. and Sothmann, B. and Burset, P. and Trauzettel, B.*Physical Review B*95 (2017)We propose a novel scanning tunneling microscope (STM) device in which the tunneling tip is formed by a Majorana bound state (MBS). This peculiar bound state emerges at the boundary of a one-dimensional topological superconductor. Since the MBS has to be effectively spinless and local, we argue that it is the smallest unit that shows itself the properties of odd-frequency superconducting pairing. Odd-frequency superconductivity is characterized by an anomalous Green's function, which is an odd function of the time arguments of the two electrons building the Cooper pair. Interestingly, our Majorana STM can be used as the perfect detector of odd-frequency superconductivity. The reason is that a supercurrent between the Majorana STM and any other superconductor can only flow if the latter system exhibits itself odd-frequency pairing. To illustrate our general idea, we consider the tunneling problem of the Majorana STM coupled to a quantum dot placed on a surface of a conventional superconductor.view abstract 10.1103/PhysRevB.95.174516 **Optimal Quantum Interference Thermoelectric Heat Engine with Edge States**

Samuelsson, P. and Kheradsoud, S. and Sothmann, B.*Physical Review Letters*118 (2017)We show theoretically that a thermoelectric heat engine, operating exclusively due to quantum-mechanical interference, can reach optimal linear-response performance. A chiral edge state implementation of a close-to-optimal heat engine is proposed in an electronic Mach-Zehnder interferometer with a mesoscopic capacitor coupled to one arm. We demonstrate that the maximum power and corresponding efficiency can reach 90% and 83%, respectively, of the theoretical maximum. The proposed heat engine can be realized with existing experimental techniques and has a performance robust against moderate dephasing. © 2017 American Physical Society.view abstract 10.1103/PhysRevLett.118.256801 **A dosimetric comparison of real-time adaptive and non-adaptive radiotherapy: A multi-institutional study encompassing robotic, gimbaled, multileaf collimator and couch tracking**

Colvill, E. and Booth, J. and Nill, S. and Fast, M. and Bedford, J. and Oelfke, U. and Nakamura, M. and Poulsen, P. and Worm, E. and Hansen, R. and Ravkilde, T. and Rydhog, J. S. and Pommer, T. and af Rosenschold, P. M. and Lang, S. and Guckenberger, M. and Groh, C. and Herrmann, C. and Verellen, D. and Poels, K. and Wang, L. and Hadsell, M. and Sothmann, T. and Blanck, O. and Keall, P.*Radiotherapy and Oncology*119 (2016)Purpose: A study of real-time adaptive radiotherapy systems was performed to test the hypothesis that, across delivery systems and institutions, the dosimetric accuracy is improved with adaptive treatments over non-adaptive radiotherapy in the presence of patient-measured tumor motion. Methods and materials: Ten institutions with robotic(2), gimbaled(2), MLC(4) or couch tracking(2) used common materials including CT and structure sets, motion traces and planning protocols to create a lung and a prostate plan. For each motion trace, the plan was delivered twice to a moving dosimeter; with and without real-time adaptation. Each measurement was compared to a static measurement and the percentage of failed points for gamma-tests recorded. Results: For all lung traces all measurement sets show improved dose accuracy with a mean 2%/2 mm gamma-fail rate of 1.6% with adaptation and 15.2% without adaptation (p < 0.001). For all prostate the mean 2%/2 mm gamma-fail rate was 1.4% with adaptation and 17.3% without adaptation (p < 0.001). The difference between the four systems was small with an average 2%/2 mm gamma-fail rate of <3% for all systems with adaptation for lung and prostate. Conclusions: The investigated systems all accounted for realistic tumor motion accurately and performed to a similar high standard, with real-time adaptation significantly outperforming non-adaptive delivery methods. (C) 2016 The Authors. Published by Elsevier Ireland Ltd.view abstract 10.1016/j.radonc.2016.03.006 **Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics**

Sánchez, R. and Sothmann, B. and Jordan, A.N.*Physica E: Low-Dimensional Systems and Nanostructures*75 (2016)A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime. © 2015 Elsevier B.V. All rights reserved.view abstract 10.1016/j.physe.2015.09.004 **Fingerprint of topological Andreev bound states in phase-dependent heat transport**

Sothmann, B. and Hankiewicz, E.M.*Physical Review B*94 (2016)We demonstrate that phase-dependent heat currents through superconductor-topological insulator Josephson junctions provide a useful tool to probe the existence of topological Andreev bound states, even for multichannel surface states. We predict that in the tunneling regime topological Andreev bound states lead to a minimum of the thermal conductance for a phase difference φ=π, in clear contrast to a maximum of the thermal conductance at φ=π that occurs for trivial Andreev bound states in superconductor-normal-metal tunnel junctions. This opens up the possibility that phase-dependent heat transport can distinguish between topologically trivial and nontrivial 4π modes. Furthermore, we propose a superconducting quantum interference device geometry where phase-dependent heat currents can be measured using available experimental technology. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.081407 **Thermoelectrics with Coulomb-coupled quantum dots**

Thierschmann, H. and Sánchez, R. and Sothmann, B. and Buhmann, H. and Molenkamp, L.W.*Comptes Rendus Physique*17 (2016)In this article we review the thermoelectric properties of three terminal devices with Coulomb-coupled quantum dots (QDs) as observed in recent experiments [1,2]. The system we consider consists of two Coulomb-blockade QDs, one of which can exchange electrons with only a single reservoir (heat reservoir), while the other dot is tunnel coupled with two reservoirs at a lower temperature (conductor). The heat reservoir and the conductor interact only via the Coulomb coupling of the quantum dots. It has been found that two regimes have to be considered. In the first one, the heat flow between the two systems is small. In this regime, thermally driven occupation fluctuations of the hot QD modify the transport properties of the conductor system. This leads to an effect called thermal gating. Experiments have shown how this can be used to control charge flow in the conductor by means of temperature in a remote reservoir. We further substantiate the observations with model calculations, and implications for the realisation of an all-thermal transistor are discussed. In the second regime, the heat flow between the two systems is relevant. Here the system works as a nanoscale heat engine, as proposed recently (Sánchez and Büttiker [3]). We review the conceptual idea, its experimental realisation and the novel features arising in this new kind of thermoelectric device such as decoupling of heat and charge flow. © 2016 Académie des sciencesview abstract 10.1016/j.crhy.2016.08.001 **Chiral thermoelectrics with quantum hall edge states**

Sánchez, R. and Sothmann, B. and Jordan, A.N.*Physical Review Letters*114 (2015)The thermoelectric properties of a three-terminal quantum Hall conductor are investigated. We identify a contribution to the thermoelectric response that relies on the chirality of the carrier motion rather than on spatial asymmetries. The Onsager matrix becomes maximally asymmetric with configurations where either the Seebeck or the Peltier coefficients are zero while the other one remains finite. Reversing the magnetic field direction exchanges these effects, which originate from the chiral nature of the quantum Hall edge states. The possibility to generate spin-polarized currents in quantum spin Hall samples is discussed. © 2015 American Physical Society.view abstract 10.1103/PhysRevLett.114.146801 **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 **Heat diode and engine based on quantum Hall edge states**

Sánchez, R. and Sothmann, B. and Jordan, A.N.*New Journal of Physics*17 (2015)We investigate charge and energy transport in a three-terminal quantum Hall conductor. The peculiar properties of chiral propagation along the edges of the sample have important consequences on the response to thermal biases. Based on the separation of charge and heat flows, thermoelectric conversion and heat rectification can be manipulated by tuning the scattering at gate-modulated constrictions. Chiral motion in a magnetic field allows for a different behavior of left-and right-moving carriers giving rise to thermal rectification by redirecting the heat flows. We propose our system both as an efficient heat-to-work converter and as a heat diode. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/17/7/075006 **Josephson response of a conventional and a noncentrosymmetric superconductor coupled via a double quantum dot**

Sothmann, B. and Tiwari, R.P.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)We consider transport through a Josephson junction consisting of a conventional s-wave superconductor coupled via a double quantum dot to a noncentrosymmetric superconductor with both singlet and triplet pairing. We calculate the Andreev bound state energies and the associated Josephson current. We demonstrate that the current-phase relation is a sensitive probe of the singlet-triplet ratio in the noncentrosymmetric superconductor. In particular, in the presence of an inhomogeneous magnetic field the system exhibits a φ-junction behavior. ©2015 American Physical Society.view abstract 10.1103/PhysRevB.92.014504 **Quantum heat engines based on electronic Mach-Zehnder interferometers**

Hofer, P.P. and Sothmann, B.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)We theoretically investigate the thermoelectric properties of heat engines based on Mach-Zehnder interferometers. The energy dependence of the transmission amplitudes in such setups arises from a difference in the interferometer arm lengths. Any thermoelectric response is thus of purely quantum-mechanical origin. In addition to an experimentally established three-terminal setup, we also consider a two-terminal geometry as well as a four-terminal setup consisting of two interferometers. We find that Mach-Zehnder interferometers can be used as powerful and efficient heat engines which perform well under realistic conditions. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.195406 **Reprint of: Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics**

Sánchez, R. and Sothmann, B. and Jordan, A.N.*Physica E: Low-Dimensional Systems and Nanostructures*(2015)A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime. © 2016.view abstract 10.1016/j.physe.2016.05.023 **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 **Thermoelectric energy harvesting with quantum dots**

Sothmann, B. and Sánchez, R. and Jordan, A.N.*Nanotechnology*26 (2015)We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics. © 2015 IOP Publishing Ltd.view abstract 10.1088/0957-4484/26/3/032001 **Three-terminal energy harvester with coupled quantum dots**

Thierschmann, H. and Sánchez, R. and Sothmann, B. and Arnold, F. and Heyn, C. and Hansen, W. and Buhmann, H. and Molenkamp, L.W.*Nature Nanotechnology*10 (2015)Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines. © 2015 Macmillan Publishers Limited. All rights reserved.view abstract 10.1038/nnano.2015.176 **Electronic waiting-time distribution of a quantum-dot spin valve**

Sothmann, B.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)We discuss the electronic waiting-time distribution of a quantum-dot spin valve, i.e., a single-level quantum dot coupled to two ferromagnetic electrodes with magnetizations that can point in arbitrary directions. We demonstrate that the rich transport physics of this setup, such as dynamical channel blockade and spin precession in an interaction-driven exchange field, shows up in the waiting-time distribution, and we analyze the conditions necessary to observe the various effects. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.155315 **Hybrid microwave-cavity heat engine**

Bergenfeldt, C. and Samuelsson, P. and Sothmann, B. and Flindt, C. and Büttiker, M.*Physical Review Letters*112 (2014)We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum-dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters. © 2014 American Physical Society.view abstract 10.1103/PhysRevLett.112.076803 **Quantum Nernst engines**

Sothmann, B. and Sánchez, R. and Jordan, A.N.*EPL*107 (2014)We theoretically propose Nernst engines based on quantum Hall edge states. We identify a setup that exhibits an extreme asymmetry between the off-diagonal Onsager coefficients for heat and charge transport. In terms of thermodynamic efficiency, this engine outperforms a recently proposed classical Nernst engine. A second setup using an antidot is found to be more efficient as energy filtering becomes less strong. © EPLA, 2014.view abstract 10.1209/0295-5075/107/47003 **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 **Correlations of heat and charge currents in quantum-dot thermoelectric engines**

Sánchez, R. and Sothmann, B. and Jordan, A.N. and Büttiker, M.*New Journal of Physics*15 (2013)We analyze the noise properties of both electric charge and heat currents as well as their correlations in a quantum-dot based thermoelectric engine. The engine is a three-terminal conductor with crossed heat and charge flows where heat fluctuations can be monitored by a charge detector. We investigate the mutual influence of charge and heat dynamics and how it is manifested in the current and noise properties. In the presence of energy-dependent tunneling, operating conditions are discussed where a charge current can be generated by heat conversion. In addition, heat can be pumped into the hot source by driving a charge current in the coupled conductor. An optimal configuration is found for structures in which the energy dependence of tunneling maximizes asymmetric transmission with maximal charge-heat cross-correlations. Remarkably, at a voltage that stalls the heat engine we find that in the optimal case the non-equilibrium state is maintained by fluctuations in the heat and charge currents only. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/12/125001 **Fractional Josephson effect in a quadruple quantum dot**

Sothmann, B. and Li, J. and Büttiker, M.*New Journal of Physics*15 (2013)A double quantum dot coupled to an s-wave superconductor and subject to an inhomogeneous magnetic field can host a pair of zero-energy Majorana fermions when the dot properties are tuned appropriately. Here, we demonstrate the possibility of generating a fractional 4π Josephson effect in two such double dots tunnel-coupled to each other. We discuss the robustness of this effect with respect to perturbations away from the special point in parameter space where the uncoupled double dots host Majorana fermions. We demonstrate the possibility of generating Josephson effects with a period of 8π and 12π in strongly coupled double dots. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/8/085018 **Powerful and efficient energy harvester with resonant-tunneling quantum dots**

Jordan, A.N. and Sothmann, B. and Sánchez, R. and Büttiker, M.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We propose a nanoscale heat engine that utilizes the physics of resonant tunneling in quantum dots in order to transfer electrons only at specific energies. The nanoengine converts heat into electrical current in a multiterminal geometry which permits one to separate current and heat flows. By putting two quantum dots in series with a hot cavity, electrons that enter one lead are forced to gain a prescribed energy in order to exit the opposite lead, transporting a single electron charge. This condition yields an ideally efficient heat engine. The energy gain is a property of the composite system rather than of the individual dots. It is therefore tunable to optimize the power while keeping a much larger level spacing for the individual quantum dots. Despite the simplicity of the physical model, the optimized rectified current and power is larger than any other candidate nanoengine. The ability to scale the power by putting many such engines into a two-dimensional layered structure gives a paradigmatic system for harvesting thermal energy at the nanoscale. We demonstrate that the high power and efficiency of the layered structure persists even if the quantum dots exhibit some randomness. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.075312 **Powerful energy harvester based on resonant-tunneling quantum wells**

Sothmann, B. and Sánchez, R. and Jordan, A.N. and Büttiker, M.*New Journal of Physics*15 (2013)We analyze a heat engine based on a hot cavity connected via quantum wells to electronic reservoirs. We discuss the output power as well as the efficiency both in the linear and nonlinear regime. We find that the device delivers a large power of about 0.18 W cm-2 for a temperature difference of 1 K, nearly doubling the power that can be extracted from a similar heat engine based on quantum dots. At the same time, the heat engine also has good efficiency albeit reduced from the quantum dot case. Due to the large level spacings that can be achieved in quantum wells, our proposal opens a route toward room-temperature applications of nanoscale heat engines. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/9/095021 **Quantized electronic heat flow**

Sothmann, B. and Flindt, C.*Science*342 (2013)A measurement of the quantum-limited heat flow in an electronic conductor opens a pathway to the nanoscale control of heat currents.view abstract 10.1126/science.1246105 **Magnon-driven quantum-dot heat engine**

Sothmann, B. and Büttiker, M.*EPL*99 (2012)We investigate a heat to charge current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nanoengine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency. Copyright © EPLA, 2012.view abstract 10.1209/0295-5075/99/27001 **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 **Rectification of thermal fluctuations in a chaotic cavity heat engine**

Sothmann, B. and Sánchez, R. and Jordan, A.N. and Büttiker, M.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)We investigate the rectification of thermal fluctuations in a mesoscopic on-chip heat engine. The engine consists of a hot chaotic cavity capacitively coupled to a cold cavity which rectifies the excess noise and generates a directed current. The fluctuation-induced directed current depends on the energy asymmetry of the transmissions of the contacts of the cold cavity to the leads and is proportional to the temperature difference. We discuss the channel dependence of the maximal power output of the heat engine and its efficiency. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.205301 **Charge ordering of magnetic dipoles in artificial honeycomb patterns**

Schumann, A. and Sothmann, B. and Szary, P. and Zabel, H.*Applied Physics Letters*97 (2010)Artificial spin ice offers the possibility to investigate a variety of dipolar orderings, spin frustrations and ground states. We have investigated magnetic dipoles arranged on a honeycomb lattice as a function of applied field, using magnetic force microscopy. The patterns were prepared by electron beam lithography where the basic units are polycrystalline Fe islands with dimensions length, width, and thickness of 3 μm, 0.3 μm, and 20 nm, respectively. These islands are in a single domain dipolar state at remanence. We have measured the magnetization reversal of the honeycomb patterns with different field directions. For the easy direction with the field parallel to one of the three dipole sublattices we observe at coercivity a maximum of magnetic charge order of alternating charges ±3, where the magnetic charge refers to the number and sign of magnetic poles pointing into any of the vertices. © 2010 American Institute of Physics.view abstract 10.1063/1.3463482 **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 **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 **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

#### mesoscopic systems

#### phase-coherent heat transport

#### quantum transport

#### thermoelectrics