[93] 
Legendre, Julian and Zsurka, Eduárd and Di Miceli, Daniele and Serra, Llorenç and Moors, Kristof and Schmidt, Thomas L., Topological Properties of FiniteSize Heterostructures of Magnetic Topological Insulators and Superconductors, arXiv:2404.16520 [condmat] (2024)
Heterostructures of magnetic topological insulators (MTIs) and superconductors (SCs) in twodimensional (2D) slab and onedimensional (1D) nanoribbon geometries have been predicted to host, respectively, chiral Majorana edge states (CMESs) and Majorana bound states (MBSs). We study the topological properties of such MTI/SC heterostructures upon variation of the geometry from wide slabs to quasi1D nanoribbon systems and as a function of the chemical potential, the magnetic doping, and the induced superconducting pairing potential. To do so, we construct effective symmetryconstrained lowenergy Hamiltonians accounting for the realspace confinement. For a nanoribbon geometry with finite width and length, we observe different phases characterized by CMESs, MBSs, as well as coexisting CMESs and MBSs, as the chemical potential, the magnetic doping and/or the width are varied.

[92] 
Zsurka, Eduárd and Wang, Cheng and Legendre, Julian and Di Miceli, Daniele and Serra, Llorenç and Grützmacher, Detlev and Schmidt, Thomas L. and Rüßmann, Philipp and Moors, Kristof, LowEnergy Modeling of ThreeDimensional Topological Insulator Nanostructures, arXiv:2404.13959 [condmat] (2024)
We develop an accurate nanoelectronic modeling approach for realistic threedimensional topological insulator nanostructures and investigate their lowenergy surfacestate spectrum. Starting from the commonly considered fourband \$\boldsymbol\\mathrm\kḑot p\\\$ bulk model Hamiltonian for the Bi\$_2\$Se\$_3\$ family of topological insulators, we derive new parameter sets for Bi\$_2\$Se\$_3\$, Bi\$_2\$Te\$_3\$ and Sb\$_2\$Te\$_3\$. We consider a fitting strategy applied to \emph\ab initio\ band structures around the \$\Gamma\$ point that ensures a quantitatively accurate description of the lowenergy bulk and surface states, while avoiding the appearance of unphysical lowenergy states at higher momenta, something that is not guaranteed by the commonly considered perturbative approach. We analyze the effects that arise in the lowenergy spectrum of topological surface states due to band anisotropy and electronhole asymmetry, yielding Dirac surface states that naturally localize on different side facets. In the thinfilm limit, when surface states hybridize through the bulk, we resort to a thinfilm model and derive thicknessdependent model parameters from \emph\ab initio\ calculations that show good agreement with experimentally resolved band structures, unlike the bulk model that neglects relevant manybody effects in this regime. Our versatile modeling approach offers a reliable starting point for accurate simulations of realistic topological materialbased nanoelectronic devices.

[91] 
Wu, Kunmin and Kadijani, Sadeq S. and Schmidt, Thomas L., Braiding of Majorana Bound States in a DrivenDissipative Majorana Box Setup, arXiv:2404.04147 [condmat] (2024)
We investigate a system of Majorana box qubits, where each of the Coulomb blockaded boxes is driven by an applied AC voltage and is embedded in a dissipative environment. The AC voltage is applied between a pair of quantum dots, each of which is coupled by tunneling to a Majorana box qubit. Moreover, the dissipation is created by the coupling to an electromagnetic environment. Recent work has shown that in this case the Majorana bound states which form the computational basis can emerge as dark states, which are stabilized by the dissipation. In our work, we show that the same platform can be used to enable topological braiding of these dissipative Majorana bound states. We show that coupling three such Majorana boxes allows a braiding transformation by changing the tunnel amplitudes adiabatically in time.

[90] 
Haller, Andreas and Díaz, Sebastián A. and Belzig, Wolfgang and Schmidt, Thomas L., Quantum Magnetic Skyrmion Operator, arXiv:2403.10347 [condmat] (2024)
We propose a variational wave function to represent quantum skyrmions as bosonic operators. The operator faithfully reproduces two fundamental features of quantum skyrmions: their classical magnetic order and a "quantum cloud" of local spinflip excitations. Using exact numerical simulations of the ground states of a 2D chiral magnetic model, we find two regions in the singleskyrmion state diagram distinguished by their leading quantum corrections. We use matrix product state simulations of the adiabatic braiding of two skyrmions to verify that the operator representation of skyrmions is valid at large interskyrmion distances. Our work demonstrates that skyrmions can be approximately coarsegrained and represented by bosonic quasiparticles, which paves the way toward a field theory of manyskyrmion quantum phases which, unlike other approaches, incorporates the microscopic quantum fluctuations of individual skyrmions.

[88] 
Engdahl, Jack N. and Keser, Aydın Cem and Schmidt, Thomas and Sushkov, Oleg P., Driving Viscous Hydrodynamics in Bulk Electron Flow in Graphene Using Micromagnets, Physical Review B 109, 195402 (2024)
We consider the hydrodynamic flow of an electron fluid in a channel formed in a twodimensional electron gas (2DEG) with noslip boundary conditions. To generate vorticity in the fluid, the flow is influenced by an array of micromagnets on the top of the 2DEG. We analyze the viscous boundary layer, and we demonstrate antiPoiseuille behavior in this region. Furthermore, we predict a longitudinal voltage modulation, where a periodic magnetic field generates a voltage term periodic in the direction of transport. From an experimental point of view, we propose a method for a boundaryindependent measurement of the viscosity of different electron fluids. The results are applicable to graphene away from the chargeneutrality point and to semiconductors.

[89] 
Kadijani, Sadeq S. and Del Grosso, Nicolás and Schmidt, Thomas L. and Farias, M. Belén, Dynamical Casimir Cooling in Circuit QED Systems, arXiv:2312.09893 [condmat, physics:quantph] (2023)
A transmission line coupled to an externally driven superconducting quantum interference device (SQUID) can exhibit the Dynamical Casimir Effect (DCE). Employing this setup, we quantize the SQUID degrees of freedom and show that it gives rise to a threebody interaction Hamiltonian with the cavity modes. By considering only two interacting modes from the cavities we show that the device can function as an autonomous cooler where the SQUID can be used as a work source to cool down the cavity modes. Moreover, this setup allows for coupling to all modes existing inside the cavities, and we show that by adding two other extra modes to the interaction with the SQUID the cooling effect can be enhanced.

[87] 
Idrisov, Edvin G. and Hasdeo, Eddwi H. and Radhakrishnan, Byjesh N. and Schmidt, Thomas L., Hydrodynamic NavierStokes Equations in TwoDimensional Systems with Rashba SpinOrbit Coupling, Low Temperature Physics 49, 1385 (2023)
We study a twodimensional (2D) electron system with a linear spectrum in the presence of Rashba spinorbit (RSO) coupling in the hydrodynamic regime. We derive a semiclassical Boltzmann equation with a collision integral due to Coulomb interactions in the basis of the eigenstates of the system with RSO coupling. Using the local equilibrium distribution functions, we obtain a generalized hydrodynamic NavierStokes equation for electronic systems with RSO coupling. In particular, we discuss the influence of the spinorbit coupling on the viscosity and the enthalpy of the system and present some of its observable effects in hydrodynamic transport.

[86] 
Kashuba, O. and Schmidt, T. L. and Hassler, F. and Haller, A. and Riwar, R.P., Counting Interacting Electrons in One Dimension, Physical Review B 108, 235133 (2023)
The calculation of the full counting statistics of the charge within a finite interval of an interacting onedimensional system of electrons is a fundamental, yet as of now, unresolved problem. Even in the noninteracting case, charge counting turns out to be more difficult than anticipated because it necessitates the calculation of a nontrivial determinant and requires regularization. Moreover, interactions in a onedimensional system are best described using bosonization. However, this technique rests on a longwavelength approximation and is a priori inapplicable for charge counting due to the sharp boundaries of the counting interval. To mitigate these problems, we investigate the counting statistics using several complementary approaches. To treat interactions, we develop a diagrammatic approach in the fermionic basis, which makes it possible to obtain the cumulant generating function up to arbitrary order in the interaction strength. Importantly, our formalism preserves charge quantization in every perturbative order. We derive an exact expression for the noise and analyze its interactiondependent logarithmic cutoff. We compare our fermionic formalism with the results obtained by other methods, such as the Wigner crystal approach and numerical calculations using the densitymatrix renormalization group. Surprisingly, we show good qualitative agreement with the Wigner crystal for weak interactions, where the latter is in principle not expected to apply.

[85] 
Cavina, Vasco and Kadijani, Sadeq S. and Esposito, Massimiliano and Schmidt, Thomas L., A Convenient Keldysh Contour for Thermodynamically Consistent Perturbative and Semiclassical Expansions, SciPost Physics 15, 209 (2023)
SciPost Journals Publication Detail SciPost Phys. 15, 209 (2023) A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions

[84] 
Di Miceli, Daniele and Zsurka, Eduárd and Legendre, Julian and Moors, Kristof and Schmidt, Thomas L. and Serra, Llorenç, Conductance Asymmetry in Proximitized Magnetic Topological Insulator Junctions with Majorana Modes, Physical Review B 108, 035424 (2023)
We theoretically discuss electronic transport via Majorana states in magnetic topological insulatorsuperconductor junctions with an asymmetric split of the applied bias voltage. We study normalsuperconductornormal (NSN) junctions made of narrow (wirelike) or wide (filmlike) magnetic topological insulator slabs with a central proximitized superconducting sector. The occurrence of chargenonconserving Andreev processes entails a nonzero conductance related to an electric current flowing to ground from the proximitized sector of the NSN junction. We show that topologically protected Majorana modes require an antisymmetry of this conductance with respect to the point of equally split bias voltage across the junction.

[83] 
Poduval, Prathyush P. and Schmidt, Thomas L. and Haller, Andreas, Perfectly Localized Majorana Corner Modes in Fermionic Lattices, Physical Review B 108, 035124 (2023)
Focusing on examples of Majorana zero modes on the corners of a twodimensional lattice, we introduce a method to find parameter regions where the Majorana modes are perfectly localized on a single site. Such a limit allows us to study the dimerization structure of the sparse bulk Hamiltonian that results in the higherorder topology of the system. Furthermore, such limits typically provide an analytical understanding of the system energy scales. Based on the dimerization structure we extract from the twodimensional model, we identify a more general stacking procedure to construct Majorana zero modes in arbitrary corners of a ddimensional hypercube, which we demonstrate explicitly in d$łeq$3.

[82] 
Haller, Andreas and Hegde, Suraj and Xu, Chen and De Beule, Christophe and Schmidt, Thomas L. and Meng, Tobias, Black Hole Mirages: Electron Lensing and Berry Curvature Effects in Inhomogeneously Tilted Weyl Semimetals, SciPost Physics 14, 119 (2023)
We study electronic transport in Weyl semimetals with spatially varying nodal tilt profiles. We find that the flow of electrons can be guided precisely by judiciously chosen tilt profiles. In a broad regime of parameters, we show that electron flow is described well by semiclassical equations of motion similar to the ones governing gravitational attraction. This analogy provides a physically transparent tool for designing tiltronic devices like electronic lenses. The analogy to gravity circumvents the notoriously difficult fullfledged description of inhomogeneous solids. A comparison to microscopic lattice simulations shows that it is only valid for trajectories sufficiently far from analogue black holes. We finally comment on the Berry curvaturedriven transverse motion and relate the latter to spin precession physics.

[81] 
Hasdeo, Eddwi H. and Idrisov, Edvin G. and Schmidt, Thomas L., Coulomb Drag of Viscous Electron Fluids: Drag Viscosity and Negative Drag Conductivity, Physical Review B 107, L121107 (2023)
We show that Coulomb drag in bilayer systems in the regime of electron hydrodynamics leads to additional viscosity terms in the hydrodynamic equations, the drag, and dragHall viscosities, besides the wellknown kinematic and Hall viscosities. These additional viscosity terms arise from a change of the stress tensor due to the interlayer Coulomb interactions. All four viscosity terms are tunable by varying the applied magnetic field and the electron densities in the two layers. At certain ratios between the electron densities in the two layers, the drag viscosity dramatically changes the longitudinal transport resulting in a negative drag conductivity.

[80] 
Michelsen, Andreas Bock and Recher, Patrik and Braunecker, Bernd and Schmidt, Thomas L., SupercurrentEnabled Andreev Reflection in a Chiral Quantum Hall Edge State, Physical Review Research 5, 013066 (2023)
A chiral quantum Hall (QH) edge state placed in proximity to an swave superconductor experiences induced superconducting correlations. Recent experiments have observed the effect of proximity coupling in QH edge states through signatures of the mediating process of Andreev reflection. We present the microscopic theory behind this effect by modeling the system with a manybody Hamiltonian, consisting of an swave superconductor, subject to spinorbit coupling and a magnetic field, which is coupled by electron tunneling to an integer QH edge state. By integrating out the superconductor we obtain an effective pairing Hamiltonian in the QH edge state. We clarify the qualitative appearance of nonlocal superconducting correlations in a chiral edge state and analytically predict the suppression of electronhole conversion at low energies (Pauli blocking) and negative resistance as experimental signatures of Andreev reflection in this setup. In particular, we show how two surface phenomena of the superconductor, namely, Rashba spinorbit coupling and a supercurrent due to the Meissner effect, are essential for the Andreev reflection. Our work provides a promising pathway to the realization of Majorana zero modes and their parafermionic generalizations.

[79] 
Haller, Andreas and Groenendijk, Solofo and Habibi, Alireza and Michels, Andreas and Schmidt, Thomas L., Quantum Skyrmion Lattices in Heisenberg Ferromagnets, Physical Review Research 4, 043113 (2022)
Skyrmions are topological magnetic textures that can arise in noncentrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with nanometer length scales has sparked interest in their quantum properties. Here, we simulate the ground states of twodimensional spin1/2 Heisenberg lattices with DzyaloshinskiiMoriya interactions and discover a broad region in the zerotemperature phase diagram which hosts quantum skyrmion lattices. We argue that the quantum skyrmion lattice phase can be detected experimentally in the magnetization profile via local magnetic polarization measurements as well as in the spin structure factor measurable via neutron scattering experiments. Finally, we explore the resulting quantum skyrmion state, analyze its realspace polarization profile and show that it is a nonclassical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion.

[78] 
Teixeira, Raphael L. R. C. and Haller, Andreas and Singh, Roshni and Mathew, Amal and Idrisov, Edvin G. and Dias da Silva, Luis G. G. V. and Schmidt, Thomas L., Overlap of Parafermionic Zero Modes at a Finite Distance, Physical Review Research 4, 043094 (2022)
Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zeroenergy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the groundstate degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying Z2n symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute oneinstanton gas approximation and show how finitesize effects can give rise to higherorder parafermion interactions. We find good quantitative agreement between the analytical results and Monte Carlo simulations. We estimate that these finitesize corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.

[77] 
Wu, Kunmin and Schmidt, Thomas L. and Farias, M. Belén, Quantum Friction between Metals in the Hydrodynamic Regime, Physical Review A 106, 012811 (2022)
In this work, we study the phenomenon of quantum friction in a system consisting on an atom moving at a constant speed parallel to a metallic plate. We use a hydrodynamic model to describe the degrees of freedom of a clean metal without internal dissipation. We model the polarizable atom as a twolevel system with a unique (l=0) ground state and a threefold degenerate (l=1) excited state. We show that a quantum frictional force is present even in the absence of intrinsic damping in the metal, but that there is a threshold in the relative velocity that gives rise to such a force. In particular, we find that for friction to occur, the atom must move at a velocity larger than the effective speed of sound in the material, a condition that can be reached near empty or filled bands, where the Fermi velocity (which is proportional to the sound speed) becomes low. We provide analytical arguments to show that this result holds at all orders in perturbation theory.

[76] 
Idrisov, Edvin G. and Levkivskyi, Ivan P. and Sukhorukov, Eugene V. and Schmidt, Thomas L., Current Cross Correlations in a Quantum Hall Collider at Filling Factor Two, Physical Review B 106, 085405 (2022)
We use the nonequilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall edge states at filling factor $ν$=2. The current cross correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a nonanalytical dependence on the source transparency, which scales as log(1/Ts) at small Ts$łl$1. This is a consequence of electronelectron interactions in the outgoing nonequilibrium states of the collider.

[75] 
Habibi, Alireza and Musthofa, Ahmad Z. and Adibi, Elaheh and Ekström, Johan and Schmidt, Thomas L. and Hasdeo, Eddwi H., Kerr and Faraday Rotations in Topological Flat and Dispersive Band Structures, New Journal of Physics 24, 063003 (2022)
Integer quantum Hall (IQH) states and quantum anomalous Hall (QAH) states show the same static dc response but distinct dynamical ac response. In particular, the ac anomalous Hall conductivity profile $σ$ yx ($ømega$) is sensitive to the band shape of QAH states. For example, dispersive QAH bands shows resonance profile without a sign change at the band gap while the IQH states shows the sign change resonance at the cyclotron energy. We argue by flattening the dispersive QAH bands, $σ$ yx ($ømega$) should recover to that of flat Landau bands in IQH, thus it is necessary to know the origin of the sign change. Taking a topological lattice model with tunable bandwidth, we found that the origin of the sign change is not the band gap but the van Hove singularity energy of the QAH bands. In the limit of small bandwidth, the flat QAH bands recovers $σ$ yx ($ømega$) of the IQH Landau bands. Because of the Hall response, these topological bands exhibit giant polarization rotation and ellipticity in the reflected waves (Kerr effect) and rotation in the order of fine structure constant in the transmitted waves (Faraday effect) with profile resembles $σ$ yx ($ømega$). Our results serve as a simple guide to optical characterization for topological flat bands.

[74] 
De Beule, Christophe and Groenendijk, Solofo and Meng, Tobias and Schmidt, Thomas L., Artificial Event Horizons in Weyl Semimetal Heterostructures and Their NonEquilibrium Signatures, SciPost Phys. 11, 095 (2021)
We investigate transport in typeI/typeII Weyl semimetal heterostructures that realize effective black or whitehole event horizons. We provide an exact solution to the scattering problem at normal incidence and low energies, both for a sharp and a slowlyvarying Weyl cone tilt profile. In the latter case, we find two channels with transmission amplitudes analogue to those of Hawking radiation. Whereas the Hawkinglike signatures of these two channels cancel in equilibrium, we demonstrate that one can favor the contribution of either channel using a nonequilibrium state, either by irradiating the typeII region or by coupling it to a magnetic lead. This in turn gives rise to a peak in the twoterminal differential conductance which can serve as an experimental indicator of the artificial event horizon.

[73] 
Farias, M. Belén and Groenendijk, Solofo and Schmidt, Thomas L., Generalized Chern Numbers Based on Open System Green's Functions, New Journal of Physics 23, 073009 (2021)
We present an alternative approach to studying topology in open quantum systems, relying directly on Green's functions and avoiding the need to construct an effective nonHermitian (nH) Hamiltonian. We define an energydependent Chern number based on the eigenstates of the inverse Green's function matrix of the system which contains, within the selfenergy, all the information about the influence of the environment, interactions, gain or losses. We explicitly calculate this topological invariant for a system consisting of a single 2D Dirac cone and find that it is halfinteger quantized when certain assumptions about the selfenergy are made. Away from these conditions, which cannot or are not usually considered within the formalism of nH Hamiltonians, we find that such a quantization is usually lost and the Chern number vanishes, and that in special cases, it can change to integer quantization.

[72] 
Ekström, Johan and Hasdeo, Eddwi H. and Farias, M. Belén and Schmidt, Thomas L., Kerr Effect in Tilted Nodal Loop Semimetals, Physical Review B 104, 125411 (2021)
We investigate the optical activity of tilted nodal loop semimetals. We calculate the full conductivity matrix for a band structure containing a nodal loop with possible tilt in the xy plane, which allows us to study the Kerr rotation and ellipticity both for a thin film and a bulk material. We find signatures in the Kerr signal that give direct information about the tilt velocity and direction, the radius of the nodal loop, and the internal chemical potential of the system. These findings should serve as a guide to understanding optical measurements of nodal loop semimetals and as an additional tool to characterize them.

[71] 
Kölzer, Jonas and Moors, Kristof and Jalil, Abdur Rehman and Zimmermann, Erik and Rosenbach, Daniel and Kibkalo, Lidia and Schüffelgen, Peter and Mussler, Gregor and Grützmacher, Detlev and Schmidt, Thomas L. and Lüth, Hans and Schäpers, Thomas, InPlane Magnetic FieldDriven Symmetry Breaking in Topological InsulatorBased ThreeTerminal Junctions, Commun. Mater. 2, 116 (2021)
Topological surface states of threedimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbonbased circuits are threeterminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an inplane magnetic field, the orbital effect cannot be neglected when the surface states are confined to the boundary of a nanoribbon geometry. Here, we report on the magnetotransport properties of such threeterminal junctions. We observe a dependence of the current on the inplane magnetic field, with a distinct steering pattern of the surface state current towards a preferred output terminal for different magnetic field orientations. We demonstrate that this steering effect originates from the orbital effect, trapping the phasecoherent surface states in the different legs of the junction on opposite sides of the nanoribbon and breaking the leftright symmetry of the transmission across the junction. The reported magnetotransport properties demonstrate that an inplane magnetic field is not only relevant but also very useful for the characterization and manipulation of transport in threedimensional topological insulator nanoribbonbased junctions and circuits, acting as a topoelectric current switch.

[70] 
Hasdeo, Eddwi H. and Ekström, Johan and Idrisov, Edvin G. and Schmidt, Thomas L., Electron Hydrodynamics of TwoDimensional Anomalous Hall Materials, Physical Review B 103, 125106 (2021)
We study twodimensional (2D) electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective NavierStokes equation for viscous electron flow in topological materials. For small electric fields, the Hall current becomes negligible compared to the viscous longitudinal current. In this regime, we highlight an unconventional Poiseuille flow with an asymmetric profile and a deviation of the maximum of the current from the center of the system. In a 2D infinite geometry, the Berry curvature leads to current whirlpools and an asymmetry of the potential profile. This phenomenon can be probed by measuring the asymmetric nonlocal resistance profile.

[69] 
Groenendijk, Solofo and Schmidt, Thomas L. and Meng, Tobias, Universal Hall Conductance Scaling in NonHermitian Chern Insulators, Physical Review Research 3, 023001 (2021)
We investigate the Hall conductance of a twodimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic nonanalytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power law with a power 3/2 as a function of Dirac mass, chemical potential, and gain strength. Our results pave the way for the study of nonHermitian topology in fermionic transport experiments.

[68] 
Ayukaryana, Nur R. and Fauzi, Mohammad H. and Hasdeo, Eddwi H., The Quest and Hope of Majorana Zero Modes in Topological Superconductor for FaultTolerant Quantum Computing: An Introductory Overview, AIP Conference Proceedings 2382, 020007 (2021)
Ettore Majorana, in his short life, unintendedly has uncovered the most profound problem in quantum computation by his discovery of Majorana fermion, a particle which is its own antiparticle. Owing to its nonAbelian exchange statistics, Majorana fermions may act as a qubit for a universal quantum computer which is faulttolerant. The existence of such particle is predicted in midgap states (zero modes) of a topological superconductor as bound states that have a highly entangled degenerate ground state. This introductory overview will focus on the simplest theoretical proposals of Majorana fermions for topological quantum computing in superconducting systems, emphasizing the quest from the scalability problem of quantum computer to its possible solution with topological quantum computer employing nonAbelian anyons on various platforms of certain Majorana fermion signature encountered.

[67] 
Rendy, Bernardus and Hasdeo, Eddwi H., Strain Effects on Band Structure and Dirac NodalLine Morphology of ZrSiSe, J. Appl. Phys. 129, 014306 (2020)
The Dirac nodalline semimetals (DNLS) are new promising materials for technological applications due to its exotic properties, which originate from band structures dispersion and nodalline behavior. We report a study on effects of several possibilities of strains in ZrSiSe DNLS on band structure dispersion and nodalline behavior through the means of the density functional theory (DFT) calculations. We found that the Dirac nodalline of ZrSiSe is robust to all strain with reasonable magnitude. Although, there are significant changes in gap, amplitude, and energy relative to Fermi energy. We also found the effective strains to tune the nodalline and band structures are equibiaxial tensile, uniaxial (100) tensile, and uniaxial (110) tensile strain.

[66] 
Kadijani, Sadeq S. and Schmidt, Thomas L. and Esposito, Massimiliano and Freitas, Nahuel, Heat Transport in Overdamped Quantum Systems, Phys. Rev. B 102, 235422 (2020)
We obtain an analytical expression for the heat current between two overdamped quantum oscillators interacting with local thermal baths at different temperatures. The total heat current is split into classical and quantum contributions. We show how to evaluate both contributions by taking advantage of the timescale separation associated with the overdamped regime and without assuming the usual weakcoupling and Markovian approximations. We find that nontrivial quantum corrections survive even when the temperatures are high compared to the frequency scale relevant for the overdamped dynamics of the system.

[65] 
Michelsen, Andreas B. and Schmidt, Thomas L. and Idrisov, Edvin G., Current Correlations of CooperPair Tunneling into a Quantum Hall System, Phys. Rev. B 102, 125402 (2020)
We study Cooperpair transport through a quantum point contact between a superconductor and a quantum Hall edge state at integer and fractional filling factors. We calculate the tunneling current and its finitefrequency noise to the leading order in the tunneling amplitude for dc and ac bias voltage in the limit of low temperatures. At zero temperature and in the case of tunneling into a single edge channel both the conductance and differential shot noise vanish as a result of the Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a nonzero conductance and shot noise are revealed.

[64] 
Farias, M. Belén and Zyuzin, Alexander A. and Schmidt, Thomas L., Casimir Force between Weyl Semimetals in a Chiral Medium, Phys. Rev. B 101, 235446 (2020)
We study the Casimir effect in a system composed of two Weyl semimetals (WSMs) separated by a gap filled with a chiral medium. We calculate the optical response of the material to chiral photons in order to calculate the Casimir force. We find that if the medium between the two WSMs is a Faraday material, a repulsive Casimir force can be obtained. The magnitude of this repulsive force is found to be greatly enhanced at distances of a few microns, when experimentally accessible parameters are used. Moreover, in the system under consideration various parameters can be modified. Some of them are intrinsic to the materials employed (the absolute value of the Hall conductivity of the WSM, the Verdet constant of the Faraday material), while some of them can be manipulated externally even for a fixed sample, such as the external magnetic field and the orientation of the plates which determines the sign of their conductivity. Suitable combinations of these parameters can be used to switch from attraction to repulsion, and to place the trapping distance, in which no force acts on the plates, at any desired distance between them.

[63] 
Suprayoga, E. and Putri, W. B. K. and Singsoog, K. and Paengson, S. and Hanna, M. Y. and Nugraha, A. R. T. and Munazat, D. R. and Kurniawan, B. and Nurhuda, M. and Seetawan, T. and Hasdeo, E. H., Characterization of Electron and Phonon Transports in BiDoped CaMnO3 for Thermoelectric Applications, arXiv:2001.08443 [condmat.meshall] (2020)
Electron and phonon transports in CaMnO3 and its Bidoped counterpart, Bi0.03Ca0.97MnO3, are investigated by thermoelectric transport measurements, Raman spectroscopy, and firstprinciples calculations. In particular, we focus on CaMnO3 and Bi0.03Ca0.97MnO3's electronic structures, temperaturedependent electron and phonon lifetimes, and their sound velocities. We find that the antiferromagnetic insulator CaMnO3 breaks the WiedemannFranz (WF) law with the Lorenz number reaching four times that of ordinary metals at room temperature. Bismuth doping reduces both the electrical resistivity and the Seebeck coefficient of CaMnO3, thus it recovers the WF law behavior. Raman spectroscopy confirms that Bi0.03Ca0.97MnO3 has a lower Debye frequency as well as a shorter phonon lifetime. As a result, Bi0.03Ca0.97MnO3 exhibits superior thermoelectric properties over the
pristine CaMnO3 due to the lower thermal conductivity and electronic resistivity.

[62] 
Schmidt, Thomas L., Bosonization for Fermions and Parafermions, Eur. Phys. J. Special Topics 229, 621 (2020)
Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electronelectron interactions. Compared to Majorana bound states, they offer richer nonAbelian braiding statistics, and have thus been proposed as building blocks for topologically protected universal quantum computation. In this review, we provide a pedagogical introduction to the field of parafermion bound states in onedimensional systems. We present the necessary theoretical tools for their study, in particular bosonization and the renormalizationgroup technique, and show how those can be applied to study parafermions.

[61] 
Ekström, Johan and Recher, Patrik and Schmidt, Thomas L., Transport Properties of Coupled Majorana Bound States in the Coulomb Blockade Regime, Phys. Rev. B 101, 195420 (2020)
Topologically protected qubits based on nanostructures hosting Majorana bound states (MBSs) hold great promise for faulttolerant quantum computing. We study the transport properties of nanowire networks hosting MBSs with a focus on the effects of the charging energy and the overlap between neighboring MBSs in short mesoscopic samples. In particular, we investigate structures hosting four MBSs such as T junctions and Majorana boxes. Using a master equation in the Markovian approximation, we discuss the leading transport processes mediated by the MBSs. Singleelectron tunneling and processes involving creation and annihilation of Cooper pairs dominate in the sequentialtunneling limit. In the cotunneling regime the charge in the MBSs is fixed and transport is governed by transitions via virtual intermediate states. Our results show that fourterminal measurements in the T junction and Majorana box geometries can be useful tools for the characterization of the properties of MBSs with finite overlaps and charging energy.

[60] 
Tschirhart, Hugo and Ong, Ernest T. S. and Sengupta, Pinaki and Schmidt, Thomas L., Phase diagram of spin1 chains with DzyaloshinskiiMoriya interaction, Phys. Rev. B 100, 195111 (2019)
We investigate an antiferromagnetic spin1 Heisenberg chain in the presence of DyzaloshinskiiMoriya interactions (DMI) and an external magnetic field. We study the resulting spin chain using a combination of numerical and analytical techniques. Using DMRG simulations to determine the spectral gap and the entanglement spectrum, we map out the phase diagram as a function of magnetic field strength and DMI strength. We provide a qualitative interpretation for these numerical findings by mapping the spin1 chain on a spin1/2 ladder and using a bosonization approach.

[59] 
Idrisov, Edvin G. and Schmidt, Thomas L., Entropy production in onedimensional quantum fluids, Phys. Rev. B 100, 165404 (2019)
We study nonequilibrium thermodynamic properties of a driven onedimensional quantum fluid by combining nonlinear Luttinger liquid theory with the quantum kinetic equation. In particular, we derive an entropy production consistent with the laws of thermodynamics for a system subject to an arbitrary perturbation varying slowly in space and time. Working in a basis of weakly interacting fermionic quasiparticles, we show that the leading contribution to the entropy production results from threeparticle collisions, and we derive its scaling law at low temperatures.

[58] 
Thomas L. Schmidt and Giacomo Dolcetto and Christopher J. Pedder and Karyn Le Hur and Peter P. Orth, Mechanical resonances of mobile impurities in a onedimensional quantum fluid, Phys. Rev. Lett. 123, 075302 (2019)
We study a onedimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong backscattering this interaction gives rise to resonances and antiresonances in the finitefrequency mobility of the impurity pair. At the antiresonances, the two impurities remain at rest even when driven by a (small) external force. At the resonances, their synchronous motion follows the external drive in phase and reaches maximum amplitude. Using a perturbative renormalization group analysis in quantum tunneling across the impurities, we study the range of validity of our model. We predict that these mechanical antiresonances are observable in experiments on ultracold atom gases confined to one dimension.

[57] 
Groenendijk, Solofo and Calzona, Alessio and Tschirhart, Hugo and Idrisov, Edvin G. and Schmidt, Thomas L., Parafermion braiding in fractional quantum Hall edge states with a finite chemical potential, Phys. Rev. B 100, 205424 (2019)
Parafermions are nonAbelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $Z_2n$ parafermions which have been predicted to emerge as localized zero modes in fractional quantum Hall systems at filling factor $ν=1/n$ (n odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.

[56] 
Kristof Moors and Thomas L. Schmidt and Oleksiy Kashuba, Supersonic flow and negative local resistance in hydrodynamic Dirac electron nozzles, arXiv:1905.01247 [condmat.meshall] (2019)
We investigate the hydrodynamic flow of strongly interacting Dirac electrons in a nozzle geometry, which can for instance be realized with graphene. We show that a nozzle can induce a transition from subsonic to supersonic flow. This transition causes a shock wave of the electrons downstream of the throat of the nozzle, which is a distinct signature of hydrodynamic transport. We demonstrate that this effect is visible in the voltage profile along the nozzle when applying a bias and thus represents a suitable experimental probe of the hydrodynamic regime. In particular, there is a section of the nozzle with pronounced negative local resistance and a discontinuity of the local voltage induced by the shock wave.

[55] 
Moors, Kristof and Zyuzin, Alexander A. and Zyuzin, Alexander Yu. and Tiwari, Rakesh P. and Schmidt, Thomas L., Disorderdriven exceptional lines and Fermi ribbons in tilted nodalline semimetals, Phys. Rev. B 99, 041116 (2019)
We consider the impact of disorder on the spectrum of threedimensional nodalline semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a nonHermitian selfenergy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorderinduced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of nonHermitian topological phases of matter.

[54] 
Calzona, Alessio and Gambetta, Filippo Maria and Carrega, Matteo and Cavaliere, Fabio and Schmidt, Thomas L. and Sassetti, Maura, Universal scaling of quenchinduced correlations in a onedimensional channel at finite temperature, SciPost Phys. 4, 023 (2018)
It has been shown that a quantum quench of interactions in a onedimensional fermion system at zero temperature induces a universal power law $∝ t^2$ in its longtime dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the nonequilibrium fermionic spectral function are considered. We show that the nonuniversal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour $∝ t^2$ is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The longtime dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the nonquenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quenchinduced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the onedimensional channel, can enhance the visibility of the universal powerlaw behaviour.

[53] 
Alessio Calzona and Tobias Meng and Maura Sassetti and Thomas L. Schmidt, Z4 parafermions in onedimensional fermionic lattices, Phys. Rev. B 98, 201110(R) (2018)
Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice Z4 parafermions and lattice spin1/2 fermions which preserves the locality of operators with Z4 symmetry. Based on this mapping, we construct an exactly solvable, local, and interacting onedimensional fermionic Hamiltonian which hosts zeroenergy modes obeying parafermionic algebra. We numerically show that this parafermionic phase remains stable in a wide range of parameters, and discuss its signatures in the fermionic spectral function.

[52] 
Wolf, Sebastian and Schmidt, Thomas L. and Rachel, Stephan, Unconventional superconductivity in the extended Hubbard model: Weakcoupling renormalization group, Phys. Rev. B 98, 174515 (2018)
We employ the weakcoupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic twodimensional lattices. Repulsive interactions usually lead to higherangular momentum Cooper pairing. By considering not only longerranged hoppings, but also nonlocal electronelectron interactions, we are able to find superconducting solutions for all irreducible representations on the square and hexagonal lattices, including extended regions of chiral topological superconductivity. For the square, triangular and honeycomb lattices, we provide detailed superconducting phase diagrams as well as the coupling strengths which quantify the corresponding critical temperatures depending on the bandstructure parameters, band filling, and interaction parameters. We discuss the sensitivity of the method with respect to the numerical resolution of the integration grid and the patching scheme. Eventually, we show how to efficiently reach a high numerical accuracy.

[51] 
Groenendijk, Solofo and Dolcetto, Giacomo and Schmidt, Thomas L., Fundamental limits to helical edge conductivity due to spinphonon scattering, Phys. Rev. B 97, 241406 (2018)
We study the effect of electronphonon interactions on the electrical conductance of a helical edge state of a twodimensional topological insulator. We show that the edge deformation caused by bulk acoustic phonons modifies the spin texture of the edge state, and that the resulting spinphonon coupling leads to inelastic backscattering which makes the transport diffusive. Using a semiclassical Boltzmann equation we compute the electrical conductivity and show that it exhibits a metallic BlochGrüneisen law. At temperatures on the order of the Debye temperature of the host material, spinphonon scattering thus drastically lowers the conductivity of the edge state. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $δ G ∝ T^5$ at low temperatures. Relying only on parallel transport of the helical spin texture along the deformed edge, the coupling strength is determined by the host material's density and sound velocity. Our results impose fundamental limits for the finitetemperature conductivity of a helical edge channel.

[50] 
Moors, Kristof and Schüffelgen, Peter and Rosenbach, Daniel and Schmitt, Tobias and Schäpers, Thomas and Schmidt, Thomas L., Magnetotransport signatures of threedimensional topological insulator nanostructures, Phys. Rev. B 97, 245429 (2018)
We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Yjunctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field, and the spinmomentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channels are pierced by a halfinteger magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A rightangle kink shows a unique $π$periodic magnetoconductance signature as a function of the inplane angle of the magnetic field. For a Yjunction, the transmission can be perfectly steered to either of the two possible output legs by a proper alignment of the external magnetic field. These magnetotransport signatures offer new ways to explore topological surface states and could be relevant for quantum transport experiments on nanostructures which can be realized with existing fabrication methods.

[49] 
Strasberg, Philipp and Schaller, Gernot and Schmidt, Thomas L. and Esposito, Massimiliano, Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strongcoupling regime, Phys. Rev. B 97, 205405 (2018)
We establish a theoretical method which goes beyond the weakcoupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the systembath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wideband limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulombcoupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weakcoupling description. Our numerical findings reveal that in the regime of strong coupling and nonMarkovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

[48] 
Haughian, Patrick and Esposito, Massimiliano and Schmidt, Thomas L., Quantum thermodynamics of the resonantlevel model with driven systembath coupling, Phys. Rev. B 97, 085435 (2018)
We study nonequilibrium thermodynamics in a fermionic resonantlevel model with arbitrary coupling strength to a fermionic bath, taking the wideband limit. In contrast to previous theories, we consider a system where both the level energy and the coupling strength depend explicitly on time. We find that, even in this generalized model, consistent thermodynamic laws can be obtained, up to the second order in the drive speed, by splitting the coupling energy symmetrically between system and bath. We define observables for the system energy, work, heat, and entropy, and calculate them using nonequilibrium Green's functions. We find that the observables fulfill the laws of thermodynamics, and connect smoothly to the known equilibrium results.

[47] 
Patrick Haughian and Han Hoe Yap and Jiangbin Gong and Thomas L. Schmidt, Charge pumping in strongly coupled molecular quantum dots, Phys. Rev. B 96, 195432 (2017)
The interaction between electrons and the vibrational degrees of freedom of a molecular quantum dot can lead to an exponential suppression of the conductance, an effect which is commonly termed FranckCondon blockade. Here, we investigate this effect in a quantum dot driven by timeperiodic gate voltages and tunneling amplitudes using nonequilibrium Green's functions and a Floquet expansion. Building on previous results showing that driving can lift the FranckCondon blockade, we investigate driving protocols which can be used to pump charge across the quantum dot. In particular, we show that due to the strongly coupled nature of the system, the pump current at resonance is an exponential function of the drive strength.

[46] 
Christopher J. Pedder and Tobias Meng and Rakesh Tiwari and Thomas L. Schmidt, Missing Shapiro steps and the $8π$periodic Josephson effect in interacting helical electron systems, Phys. Rev. B 96, 165429 (2017)
Twoparticle backscattering in timereversal invariant interacting helical electron systems can lead to the formation of quasiparticles with charge $e/2$. We propose a way to detect such states by means of the Josephson effect in the presence of proximityinduced superconductivity. In this case, the existence of $e/2$ charges leads to an $8π$periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit timereversal symmetry breaking, which causes the twoparticle backscattering to be a subleading effect at low energies, its presence can still be detected in driven, currentbiased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of nonAbelian zeroenergy states. We suggest that this effect can be measured in current stateoftheart Rashba wires.

[45] 
Acciai, Matteo and Calzona, Alessio and Dolcetto, Giacomo and Schmidt, Thomas L. and Sassetti, Maura, Charge and energy fractionalization mechanism in onedimensional channels, Phys. Rev. B 96, 075144 (2017)
We study the problem of injecting single electrons into interacting onedimensional quantum systems, a fundamental building block for electron quantum optics. It is well known that such injection leads to charge and energy fractionalization. We elucidate this concept by calculating the nonequilibrium electron distribution function in the momentum and energy domains after the injection of an energyresolved electron. Our results shed light on how fractionalization occurs via the creation of particlehole pairs by the injected electron. In particular, we focus on systems with a pair of counterpropagating channels, and we fully analyze the properties of each chiral fractional excitation which is created by the injection. We suggest possible routes to access their energy and momentum distribution functions in topological quantum Hall or quantum spinHall edge states.

[44] 
Kornich, Viktoriia and Pedder, Christopher J. and Schmidt, Thomas L., Spinorbit coupling in quasionedimensional Wigner crystals, Phys. Rev. B 95, 045413 (2017)
We study the effect of Rashba spinorbit coupling (SOC) on the charge and spin degrees of freedom of a quasionedimensional (quasi1D) Wigner crystal. As electrons in a quasi1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between the density of electrons and the inverse Rashba length. We present how the lowenergy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that the spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian anymore and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of a Wigner crystal in this limit.

[43] 
Ehud Amitai and Rakesh P. Tiwari and Stefan Walter and Thomas L. Schmidt and Simon E. Nigg, Nonlocal quantum state engineering with the Cooper pair splitter beyond the Coulomb blockade regime, Phys. Rev. B 93, 075421 (2016)
A Cooper pair splitter consists of two quantum dots sidecoupled to a conventional superconductor. Usually, the quantum dots are assumed to have a large charging energy compared to the superconducting gap, in order to suppress processes other than the coherent splitting of Cooper pairs. In this work, in contrast, we investigate the limit in which the charging energy is smaller than the superconducting gap. This allows us, in particular, to study the effect of a Zeeman field comparable to the charging energy. We find analytically that in this parameter regime the superconductor mediates an interdot tunneling term with a spin symmetry determined by the Zeeman field. Together with electrostatically tunable quantum dots, we show that this makes it possible to engineer a spin triplet state shared between the quantum dots. Compared to previous works, we thus extend the capabilities of the Cooper pair splitter to create entangled nonlocal electron pairs.

[42] 
Christoph P. Orth and Tibor Sekera and Christoph Bruder and Thomas L. Schmidt, The topological Anderson insulator phase in the KaneMele model, Sci. Rep. 6, 24007 (2016)
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the BernevigHughesZhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the KaneMele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowestorder Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

[41] 
Dolcetto, Giacomo and Sassetti, Maura and Schmidt, Thomas L., Edge physics in twodimensional topological insulators, Rivista del Nuovo Cimento 39, 113 (2016)
Topology in condensed matter physics manifests itself in the emergence
of edge or surface states protected by underlying symmetries. We review
twodimensional topological insulators whose onedimensional edge states are characterized
by spinmomentum locking and protected by timereversal symmetry. We
focus in particular on their transport properties in the presence of electron interactions,
which can allow the onset of different backscattering mechanisms, thus leading
to deviations from the quantized conductance observed in the ballistic regime. The
combined presence of helicity and electron interactions creates a new paradigm of the
onedimensional world called helical Luttinger liquid, whose theoretical properties
and experimental observations are reviewed.

[40] 
Pedder, Christopher J. and Meng, Tobias and Tiwari, Rakesh P. and Schmidt, Thomas L., Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields, Phys. Rev. B 94, 245414 (2016)
A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spinorbit coupling in nanowires. Such a “helical gap” manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunneling density of states. In this paper we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spinorbit coupling and electronelectron interactions. We show that in a quasionedimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sineGordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

[39] 
Haughian, Patrick and Walter, Stefan and Nunnenkamp, Andreas and Schmidt, Thomas L., Lifting the FranckCondon blockade in driven quantum dots, Phys. Rev. B 94, 205412 (2016)
Electronvibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as FranckCondon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electronvibron coupling strength. Here, we investigate the effect of a timedependent drive on this phenomenon, in particular the effect of an oscillatory gate voltage acting on the electronic dot level. We employ two different approaches: perturbation theory based on nonequilibrium Keldysh Green's functions and a master equation in BornMarkov approximation. In both cases, we find that the drive can lift the blockade by exciting vibrons. As a consequence, the relative change in average current grows exponentially with the drive strength.

[38] 
Schmidt, Thomas L. and Pedder, Christopher J., Helical gaps in interacting Rashba wires at low electron densities, Phys. Rev. B 94, 125420 (2016)
Rashba spinorbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap (“helical gap”) in the energy spectrum of noninteracting or weakly interacting onedimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. This changes strongly the expected signature of the helical gap in conductance measurements.

[37] 
Dolcetto, Giacomo and Schmidt, Thomas L., Emission of entangled Kramers pairs from a helical mesoscopic capacitor, Phys. Rev. B 94, 075444 (2016)
The realization of singleelectron sources in integer quantum Hall systems has paved the way for exploring electronic quantum optics experiments in solidstate devices. In this paper, we characterize a single Kramers pair emitter realized by a driven antidot embedded in a twodimensional topological insulator, where spinmomentum locked edge states can be exploited for generating entanglement. Contrary to previous proposals, the antidot is coupled to both edges of a quantum spin Hall bar, thus enabling this mesoscopic capacitor to emit an entangled twoelectron state. We study the concurrence C of the emitted state and the efficiency F of its emission as a function of the different spinpreserving and spinflipping tunnel couplings of the antidot with the edges. We show that the efficiency remains very high ($F≥ 50%$) even for maximally entangled states (C=1). We also discuss how the entanglement can be probed by means of noise measurements and violation of the ClauserHorneShimonyHolt inequality.

[36] 
Rod, Alexia and Dolcetto, Giacomo and Rachel, Stephan and Schmidt, Thomas L., Transport through a quantum spin Hall antidot as a spectroscopic probe of spin textures, Phys. Rev. B 94, 035428 (2016)
We investigate electron transport through an antidot embedded in a narrow strip of a twodimensional topological insulator. We focus on the most generic and experimentally relevant case with broken axial spin symmetry. Spinnonconservation allows additional scattering processes, which change the transport properties profoundly. We start from an analytical model for noninteracting transport, which we also compare with a numerical tightbinding simulation. We then extend this model by including Coulomb repulsion on the antidot, and we study the transport in the Coulombblockade limit. We investigate sequential tunneling and cotunneling regimes, and we find that the currentvoltage characteristic allows a spectroscopic measurement of the edgestate spin textures.

[35] 
Christoph P. Orth and Rakesh P. Tiwari and Tobias Meng and Thomas L. Schmidt, NonAbelian parafermions in timereversal invariant interacting helical systems, Phys. Rev. B 91, 081406(R) (2015)
The interplay between bulk spinorbit coupling and electronelectron interactions produces umklapp scattering in the helical edge states of a twodimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is timereversal invariant. We determine the zeroenergy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8π$ periodicity. Moreover, the bound states, which are protected by timereversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.

[34] 
Chris J. Pedder and Tobias Meng and Rakesh P. Tiwari and Thomas L. Schmidt, $8π$periodic Josephson effect in timereversal invariant interacting Rashba nanowires, arXiv:1507.08881 [condmat.meshall] (2015)
We investigate narrow quantum wires with strong Rashba spinorbit coupling and electronelectron interactions. We show that virtual transitions between subbands lead to umklapp scattering which can open a partial gap in the spectrum even in the presence of timereversal symmetry. Using the superconducting proximity effect to gap out the remaining modes, we show that the system can host zeroenergy states at its edges, which are protected by timereversal symmetry. We present the parameter regime in which these bound states will emerge. Similarly to Majorana bound states, they will produce a zerobias peak in the differential conductance. In contrast to the Majorana fermions, however, their fourfold degeneracy leads to an $8π$ periodicity of the Josephson current due to tunneling of fractionalized excitations with charge $e/2$.

[33] 
Grégory Strübi and Wolfgang Belzig and Thomas L. Schmidt and Christoph Bruder, Full counting statistics of Majorana interferometers, Physica E 74, 489 (2015)
We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained from the 4x4 scattering matrix S that relates the outgoing Dirac fermions to the incoming Dirac fermions. After presenting explicit expressions for the higherorder current correlations for a modified Hanbury BrownTwiss interferometer, we note that the cumulantgenerating function can be interpreted such that unitcharge transfer processes correspond to two independent halfcharge transfer processes, or alternatively, to two independent electronhole conversion processes. By a combination of analytical and numerical approaches, we verify that this factorization property holds for a general SO(4) scattering matrix, i.e. for a general interferometer geometry.

[32] 
Chao, SungPo and Schmidt, Thomas L. and Chung, ChungHou, Tunneling between helical Majorana modes and helical Luttinger liquids, Phys. Rev. B 91, 235125 (2015)
We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a singlepoint contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of the individual resonance peaks less universal and show modulations with different separation distance between the contacts. For small separation distance, the overall features remain similar to the case of a singlepoint contact.

[31] 
Rod, Alexia and Schmidt, Thomas L. and Rachel, Stephan, Spin texture of generic helical edge states, Phys. Rev. B 91, 245112 (2015)
We study the spin texture of a generic helical liquid, the edge modes of a twodimensional topological insulator with broken axial spin symmetry. By considering honeycomb and squarelattice realizations of topological insulators, we show that in all cases the generic behavior of a momentumdependent rotation of the spin quantization axis is realized. Here we establish this mechanism also for disk geometries with continuous rotational symmetry. Finally, we demonstrate that the rotation of spinquantization axis remains intact for arbitrary geometries, i.e., in the absence of any continuous symmetry. We also calculate the dependence of this rotation on the model and material parameters. Finally, we propose a spectroscopy measurement which should directly reveal the rotation of the spinquantization axis of the helical edge states.

[30] 
Nigg, Simon E. and Tiwari, Rakesh P. and Walter, Stefan and Schmidt, Thomas L., Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation, Phys. Rev. B 91, 094516 (2015)
Based on the BardeenCooperSchrieffer theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the photon pairs produced can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

[29] 
Gangadharaiah, Suhas and Schmidt, Thomas L. and Loss, Daniel, Structure factor of interacting onedimensional helical systems, Phys. Rev. B 89, 035131 (2014)
We calculate the dynamical structure factor $S(q,ømega)$ of a weakly interacting helical edge state in the presence of a magnetic field $B$. The latter opens a gap of width $2B$ in the singleparticle spectrum, which becomes strongly nonlinear near the Dirac point. For chemical potentials $μ>B$, the system then behaves as a nonlinear helical Luttinger liquid, and a mobileimpurity analysis reveals powerlaw singularities in $S(q,ømega)$ which depend on the interaction strength as well as on the spin texture of the edge states. For $μ

[28] 
Breyel, D. and Soller, H. and Schmidt, T. L. and Komnik, A., Detecting an exciton crystal by statistical means, Physica B 441, 33 (2014)
We investigate an ensemble of excitons in a coupled quantum well excited via an applied laser field. Using an effective disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function P(M) to create M excitons as well as their correlation function. It shows clear evidence of the existence of two phases corresponding to a liquid and a crystal phase. We demonstrate that not only the correlation function but also the distribution P(M) is very well suited to monitor this transition.

[27] 
Weithofer, Luzie and Recher, Patrik and Schmidt, Thomas L., Electron transport in multiterminal networks of Majorana bound states, Phys. Rev. B 90, 205416 (2014)
We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to Tshaped junctions of two Majorana nanowires. When the wires are in the topologically nontrivial regime, three MBS are localized near the outer ends of the wires, while one MBS is localized near the crossing point, and when the lengths of the wires are finite adjacent MBS can overlap. We propose a combination of current and crosscorrelation measurements to reveal the predicted coupling of four Majoranas in a topological T junction. Interestingly, we show that the elementary transport processes at the central lead are different compared to the outer leads, giving rise to characteristic nonlocal signatures in electronic transport. We find quantitative agreement between our analytical model and numerical simulations of a tightbinding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the crosscorrelation functions.

[26] 
Nussbaum, Jennifer and Schmidt, Thomas L. and Bruder, Christoph and Tiwari, Rakesh P., Josephson effect in normal and ferromagnetic topologicalinsulator junctions: Planar, step, and edge geometries, Phys. Rev. B 90, 045413 (2014)
We investigate Josephson junctions on the surface of a threedimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spinmomentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions. In these ferromagnetic junctions, we find an anomalous finite Josephson current at zero phase difference if the magnetization is pointing along the junction (and perpendicular to the Josephson current). An outofplane magnetization with respect to the central region of the junction opens up an exchange gap and leads to a nonmonotonic behavior of the critical Josephson current for sufficiently large magnetization as the chemical potential increases.

[25] 
Schmidt, Thomas L. and Nunnenkamp, Andreas and Bruder, Christoph, Majorana Qubit Rotations in Microwave Cavities, Phys. Rev. Lett. 110, 107006 (2013)
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional singlequbit gate. Supplemented with one braiding operation, this gate allows us to perform arbitrary singlequbit operations.

[24] 
Thomas L. Schmidt, Finitetemperature conductance of interacting quantum wires with Rashba spinorbit coupling, Phys. Rev. B 88, 235429 (2013)
We calculate the finitetemperature conductance of clean, weakly interacting onedimensional quantum wires subject to Rashba spinorbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($μ=0$), twoparticle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $μ > 0$, threeparticle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear singleparticle spectrum, and are thus not accessible using Luttinger liquid theory. We discuss the observability of these predictions in current experiments on InSb nanowires and in ``spiral liquids,'' where a spontaneous ordering of the nuclear spins at low temperatures produces an effective Rashba coupling.

[23] 
Orth, Christoph P. and Strübi, Grégory and Schmidt, Thomas L., Point contacts and localization in generic helical liquids, Phys. Rev. B 88, 165315 (2013)
We consider two helical liquids on opposite edges of a twodimensional topological insulator, which are connected by one or several local tunnel junctions. In the presence of spatially inhomogeneous Rashba spinorbit coupling, the spin of the helical edge states is momentum dependent, and this spin texture can be different on opposite edges. We demonstrate that this has a strong impact on the electron transport between the edges. In particular, in the case of many random tunnel contacts, the localization length depends strongly on the spin textures of the edge states.

[22] 
Dutt, Prasenjit and Schmidt, Thomas L. and Mora, Christophe and Le Hur, Karyn, Strongly correlated dynamics in multichannel quantum RC circuits, Phys. Rev. B 87, 155134 (2013)
We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or singleelectron box capacitively coupled to a gate and connected to a reservoir lead via several conducting channels. Depending on the engineering details of the quantum RC circuit, the number of channels contributing to transport varies, as does the form of the interchannel couplings. For lowfrequency ac transport, the chargerelaxation resistance (Rq) is a nontrivial function of the parameters of the system. However, in the vicinity of the chargedegeneracy points and for weak tunneling, we find as a result of crossmode mixing or channel asymmetry that Rq becomes universal for a metallic cavity at low temperatures, and equals the unit of quantum resistance. To prove this universality, we map the system to an effective onechannel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of nearperfect transmission using a bosonization approach. Focusing on the twochannel case, we study the effect of backscattering at the leaddot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weaktunneling regime near the chargedegeneracy points.

[21] 
Schmidt, Thomas L. and Nunnenkamp, Andreas and Bruder, Christoph, Microwavecontrolled coupling of Majorana bound states, New J. Phys. 15, 025043 (2013)
We propose microwavecontrolled rotations for qubits realized as Majorana bound states. To this end, we study an inhomogeneous Kitaev chain in a microwave cavity. The chain consists of two topologically nontrivial regions separated by a topologically trivial, gapped region. The Majorana bound states at the interfaces between the left (right) regions and the central region are coupled, and their energies are split by virtual cotunneling processes. The amplitude for these cotunneling processes decreases exponentially with the number of sites of the gapped region, and the decay length diverges as the gap of the topologically trivial region closes. We demonstrate that microwave radiation can exponentially enhance the coupling between the Majorana bound states, both for classical and quantized electric fields. By solving the appropriate Liouville equation numerically, we show that microwaves can drive Rabi oscillations in the Majorana sector. Our model emerges as an effective description of a topological semiconductor nanowire in a microwave cavity. Thus, our proposal provides an experimentally feasible way to obtain full singlequbit control necessary for universal quantum computation with Majorana qubits.

[20] 
Walter, Stefan and Trauzettel, Björn and Schmidt, Thomas L., Transport properties of double quantum dots with electronphonon coupling, Phys. Rev. B 88, 195425 (2013)
We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the interplay between strong electronphonon coupling and interdot tunneling can lead to a negative differential conductance at bias voltages exceeding the phonon frequency. Various transport properties are discussed, and we explain the physics of the occurrence of negative differential conductance in this system.

[19] 
Imambekov, Adilet and Schmidt, Thomas L. and Glazman, Leonid I., Onedimensional quantum liquids: Beyond the Luttinger liquid paradigm, Rev. Mod. Phys. 84, 1253 (2012)
For many years, the Luttinger liquid theory has served as a useful paradigm for the description of onedimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the lowenergy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermiedge singularity and the Fermiliquid theory, perturbation theory in the interaction strength, and new ways of treating finitesize properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.

[18] 
Schmidt, Thomas L. and Rachel, Stephan and von Oppen, Felix and Glazman, Leonid I., Inelastic Electron Backscattering in a Generic Helical Edge Channel, Phys. Rev. Lett. 108, 156402 (2012)
We evaluate the lowtemperature conductance of a weakly interacting onedimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperaturedependent deviation from the quantized conductance, $δ G ∝ T^4$. In addition, $δ G$ is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the BernevigHughesZhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spinorbit coupling.

[17] 
Breyel, D. and Schmidt, T. L. and Komnik, A., Rydberg crystallization detection by statistical means, Phys. Rev. A 86, 023405 (2012)
We investigate an ensemble of atoms which can be excited into a Rydberg state. Using a disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function $P(M)$ to create a certain number of Rydberg atoms $M$, as well as their paircorrelation function. Using the latter, we identify the critical interaction strength above which the system undergoes a phase transition to a Rydberg crystal. We then show that this phase transition can be detected using $P(M)$ alone.

[16] 
H. Mönig and R. Caballero and C.A. Kaufmann and T.L. Schmidt and M.Ch. LuxSteiner and S. Sadewasser, Nanoscale investigations of the electronic surface properties of Cu(In,Ga)Se$_2$ thin films by scanning tunneling spectroscopy, Solar Energy Materials and Solar Cells 95, 1537 (2011)
In this work we investigate the electronic surface properties of polycrystalline Cu(In,Ga)Se$_2$ thin films by locally resolved scanning tunneling spectroscopy (STS). From current imaging tunneling spectroscopy (CITS) maps of an area of we observe distinct granular inhomogeneities, where currentvoltage ($I(U)$) spectra differ from grain to grain and vary between metallic and semiconducting characteristics. Due to the high density of defect states at the Cu(In,Ga)Se$_2$ surface, the metallic $I(U)$ characteristics is not surprising. In the case of the semiconducting $I(U)$ characteristics, we suggest a preferential oxidation of particular grains, which passivates defect levels at the surface. This is supported by the presence of gallium and indium oxides detected by global Xray photoelectron spectroscopy. Furthermore, we recorded $I(U)$ spectra from different grains under supra band gap laser illumination, which always show semiconducting characteristics. This behavior can be explained by a saturated occupation of defect states by photoexcited charge carriers. By evaluating differential conductance $(dI/dU)$ spectra under illumination from various grains, we estimate the average surface band gap to and compare the valence band onset with results from macroscopic ultraviolet photoelectron spectroscopy. The high lateral resolution of our CITS data allows also to study electronic properties at grain boundaries, which are discussed with regard to a recent STS study on a nonoxidized sample.

[15] 
S. Maier and T. L. Schmidt and A. Komnik, Charge transfer statistics of a molecular quantum dot with strong electronphonon interaction, Phys. Rev. B 83, 085401 (2011)
We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics. By using the LangFirsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electronphonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data, the formalism is shown to capture the basic properties of the strongcoupling regime.

[14] 
Schmidt, Thomas L., Current Correlations in Quantum Spin Hall Insulators, Phys. Rev. Lett. 107, 096602 (2011)
We consider a fourterminal setup of a twodimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electronelectron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the interedge current. We show that different possible transport channels give rise to different signatures in the current noise and current crosscorrelations, which could be exploited in experiments to elucidate the interplay between electronelectron interactions and the helical nature of the edge states.

[13] 
Walter, Stefan and Schmidt, Thomas L. and Børkje, Kjetil and Trauzettel, Björn, Detecting Majorana bound states by nanomechanics, Phys. Rev. B 84, 224510 (2011)
We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a onedimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an swave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states.

[12] 
Thomas L. Schmidt and Kjetil Børkje and Christoph Bruder and Björn Trauzettel, Detection of qubitoscillator entanglement in nanoelectromechanical systems, Phys. Rev. Lett. 104, 177205 (2010)
Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg uncertainty limit. Therefore, it is just a question of time before we will routinely see true quantum effects in nanomechanical systems. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a realistic scenario making it possible to detect entanglement of a mechanical resonator and a qubit in a nanoelectromechanical setup. The detection scheme is all done by standard current and noise measurements of an atomic point contact coupled to an oscillator and a qubit. This setup could allow for the first observation of entanglement between a continuous and a discrete quantum system in the solid state.

[11] 
Thomas L. Schmidt and Adilet Imambekov and Leonid I. Glazman, Fate of 1D SpinCharge Separation Away from Fermi Points, Phys. Rev. Lett. 104, 116403 (2010)
We consider the dynamic response functions of interacting one dimensional spin$1/2$ fermions at arbitrary momenta. We build a nonperturbative zerotemperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced lowenergy spincharge separation and powerlaw threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.

[10] 
Thomas L. Schmidt and Adilet Imambekov and Leonid I. Glazman, Spincharge separation in onedimensional fermion systems beyond Luttinger liquid theory, Phys. Rev. B 82, 245104 (2010)
We develop a nonperturbative zerotemperature theory for the dynamic response functions of interacting onedimensional spin1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the powerlaw singularities of the spectral function and the charge and spindensity structure factors for arbitrary momenta and interaction strengths. The exponents characterizing the singularities are functions of momenta and differ significantly from the predictions of the linear Luttinger liquid theory. We generalize the notion of the spincharge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy.

[9] 
T. L. Schmidt and A. Komnik, Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom, Phys. Rev. B 80, 041307(R) (2009)
We analyze the full counting statistics (FCS) of a singlesite quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electronphonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the lowenergy sector, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all odd order cumulants vanish as well.

[8] 
V. Koerting and T. L. Schmidt and C. B. Doiron and B. Trauzettel and C. Bruder, Transport properties of a superconducting singleelectron transistor coupled to a nanomechanical oscillator, Phys. Rev. B 79, 134511 (2009)
We investigate a superconducting singleelectron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooperpair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linearresponse regime, we discuss and compare results of higherorder approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.

[7] 
RomanPascal Riwar and Thomas L. Schmidt, Transient dynamics of a molecular quantum dot with a vibrational degree of freedom, Phys. Rev. B 80, 125109 (2009)
We investigate the transient effects occurring in a molecular quantum dot described by an AndersonHolstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electronphonon interaction, we use perturbation theory to determine the time dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a selfconsistent timedependent meanfield approximation. These complementary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability.

[6] 
T. L. Schmidt and P. Werner and L. Mühlbacher and A. Komnik, Transient dynamics of the Anderson impurity model out of equilibrium, Phys. Rev. B 78, 235110 (2008)
We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonantlevel system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full timedependent nonlinear currentvoltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.

[5] 
T. L. Schmidt and A. Komnik and A. O. Gogolin, Hanbury BrownTwiss Correlations and Noise in the Charge Transfer Statistics through a Multiterminal Kondo Dot, Phys. Rev. Lett. 98, 056603 (2007)
We analyze the charge transfer statistics through a quantum dot in the Kondo regime, when coupled to an arbitrary number of terminals N. Special attention is paid to current cross correlations between concurring transport channels, which show distinct Hanbury Brown–Twiss antibunching for N>2 reflecting the fermionic nature of charge carriers. While this effect weakens as one moves away from the Kondo fixed point, a new type of correlations between nonconcurring channels emerges which are due entirely to the virtual polarization of the Kondo singlet. As these are not obscured by the background from fixedpoint correlations they provide a promising means for extracting information on the parameters of the underlying Fermiliquid model from the experimental data.

[4] 
T. L. Schmidt and A. Komnik and A. O. Gogolin, Full counting statistics of spin transfer through ultrasmall quantum dots, Phys. Rev. B 76, 241307(R) (2007)
We analyze the spinresolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modeling the setup by the Anderson Hamiltonian, we explicitly take into account the onsite Coulomb repulsion U. We calculate the cumulant generating function for the probability to transfer a certain number of electrons with a preselected spin orientation during a fixed time interval. With the cumulant generating function at hand, we are then able to calculate the spin current correlations, which are of utmost importance in the emerging field of spintronics. We confirm the existing results for the charge statistics and report the discovery of a different type of correlation between the spinup and down polarized electron flows, which has the potential to become a powerful instrument for the investigation of the Kondo effect in nanostructures.

[3] 
T. L. Schmidt and A. Komnik, Nonlinear transport through a dynamic impurity in a strongly interacting onedimensional electron gas, Phys. Rev. B 76, 035113 (2007)
We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly timedependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory, we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with the help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special nontrivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear currentvoltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies, we also find an enhancement of the linear conductance of the wire to values above the unitary limit G0=2e2/h.

[2] 
T. L. Schmidt and A. O. Gogolin and A. Komnik, Full counting statistics of spin transfer through the Kondo dot, Phys. Rev. B 75, 235105 (2007)
We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit the linear response, zero temperature statistics of the spin transfer is trinomial, such that all the odd moments vanish and the even moments follow a binomial distribution. On the contrary, the corresponding spinresolved distribution turns out to be binomial. The combined spin and charge statistics is also determined. In particular, we find that in the case of a finite magnetic field or an asymmetric junction the spin and charge measurements become statistically dependent. Furthermore, we analyzed the spin counting statistics of a generic Kondo dot at and around the strong coupling fixed point (the unitary limit). Comparing these results with the Toulouse limit calculation we determine which features of the latter are generic and which ones are artifacts of the spin symmetry breaking.

[1] 
T. L. Schmidt and A. Komnik, On the visibility of electronelectron interaction effects in field emission spectra, Solid State Communications 135, 455 (2005)
One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current $j(ømega)$ in field emission (FE) experiments. Its high energy tail $j_>(ømega)$ (above the Fermi edge) contains invaluable information about the nature of the electronelectron interactions inside the emitter. Thus far, $j_>(ømega)$ has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around $E_F$. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of $j_>(ømega)$. We apply our results to the FE from Luttinger liquids and singlewall carbon nanotubes.
