Michelsen, Andreas B. and Recher, Patrik and Braunecker, Bernd and Schmidt, Thomas L., Supercurrent-Enabled Andreev Reflection in a Chiral Quantum Hall Edge State, arXiv:2203.13384 [cond-mat.mes-hall] (2022)
A chiral quantum Hall (QH) edge state placed in proximity to an s-wave 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 many-body Hamiltonian, consisting of an s-wave superconductor, subject to spin-orbit coupling and a magnetic field, which is coupled by electron tunneling to a 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 electron-hole 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 spin-orbit 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.
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, arXiv:2201.08147 [cond-mat.mes-hall] (2022)
We use the non-equilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall (QH) edge states at filing factor \$\ nu = 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 non-analytical dependence on the source transparency, which scales as \$\ log(1/T_s)\$ at small \$T_s \ ll 1\$. This is the consequence of electron-electron interactions in the outgoing non-equilibrium states of the collider.
Haller, Andreas and Groenendijk, Solofo and Habibi, Alireza and Michels, Andreas and Schmidt, Thomas L., Quantum Skyrmion Lattices in Heisenberg Ferromagnets, arXiv:2112.12475 [cond-mat.str-el] (2021)
Skyrmions are topological magnetic textures which can arise in non-centrosymmetric 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. Quantum corrections to the classical magnetic textures have already been considered in the semiclassical regime. Here, we go beyond this limit by investigating quantum skyrmions in the deep quantum regime. We use density matrix renormalization group techniques to study two-dimensional spin-\$1/2\$ Heisenberg ferromagnets with Dzyaloshinskii-Moriya interactions and discover a broad region in the zero temperature phase diagram which hosts quantum skyrmion lattice ground states. We argue that this novel quantum skyrmion 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 real space polarization profile and show that it is a non-classical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion.
De Beule, Christophe and Groenendijk, Solofo and Meng, Tobias and Schmidt, Thomas L., Artificial Event Horizons in Weyl Semimetal Heterostructures and Their Non-Equilibrium Signatures, SciPost Phys. 11, 095 (2021)
We investigate transport in type-I/type-II Weyl semimetal heterostructures that realize effective black- or white-hole event horizons. We provide an exact solution to the scattering problem at normal incidence and low energies, both for a sharp and a slowly-varying Weyl cone tilt profile. In the latter case, we find two channels with transmission amplitudes analogue to those of Hawking radiation. Whereas the Hawking-like signatures of these two channels cancel in equilibrium, we demonstrate that one can favor the contribution of either channel using a non-equilibrium state, either by irradiating the type-II region or by coupling it to a magnetic lead. This in turn gives rise to a peak in the two-terminal differential conductance which can serve as an experimental indicator of the artificial event horizon.
Habibi, Alireza and Musthofa, Ahmad Z. and Adibi, Elaheh and Ekström, Johan and Schmidt, Thomas L. and Hasdeo, Eddwi H., Optical Properties of Topological Flat and Dispersive Bands, arXiv:2103.15085 [cond-mat.mes-hall] (2021)
We study the optical properties of topological flat and dispersive bands. Due to their topological nature, there exists an anomalous Hall response which gives rise to a transverse current without applied magnetic field. The dynamical Hall conductivity of systems with flat bands exhibits a sign change when the excitation energy is on resonance with the band gap, similar to the magnetotransport Hall conductivity profile. The sign change of the Hall conductivity is located at the frequency corresponding to the singularity of the joint density of states, i.e., the van Hove singularity (VHS). For perfectly flat bands, this VHS energy matches the band gap. On the other hand, in the case of dispersive bands, the VHS energy is located above the band gap. As a result, the two features of the Hall conductivity, i.e., the resonant feature at the band gap and the sign change at the VHS energy, become separated. This anomalous Hall response rotates the polarization of an electric field and can be detected in the reflected and transmitted waves, as Kerr and Faraday rotations, respectively, thus allowing a simple optical characterization of topological flat bands.
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 non-Hermitian (nH) Hamiltonian. We define an energy-dependent Chern number based on the eigenstates of the inverse Green's function matrix of the system which contains, within the self-energy, 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 half-integer quantized when certain assumptions about the self-energy 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.
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 x-y 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.
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, In-Plane Magnetic Field-Driven Symmetry Breaking in Topological Insulator-Based Three-Terminal Junctions, Commun. Mater. 2, 116 (2021)
Topological surface states of three-dimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbon-based circuits are three-terminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an in-plane 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 three-terminal junctions. We observe a dependence of the current on the in-plane 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 phase-coherent surface states in the different legs of the junction on opposite sides of the nanoribbon and breaking the left-right symmetry of the transmission across the junction. The reported magnetotransport properties demonstrate that an in-plane magnetic field is not only relevant but also very useful for the characterization and manipulation of transport in three-dimensional topological insulator nanoribbon-based junctions and circuits, acting as a topoelectric current switch.
Hasdeo, Eddwi H. and Ekström, Johan and Idrisov, Edvin G. and Schmidt, Thomas L., Electron Hydrodynamics of Two-Dimensional Anomalous Hall Materials, Physical Review B 103, 125106 (2021)
We study two-dimensional (2D) electron systems in the hydrodynamic regime. We show that a geometrical Berry curvature modifies the effective Navier-Stokes 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.
Groenendijk, Solofo and Schmidt, Thomas L. and Meng, Tobias, Universal Hall Conductance Scaling in Non-Hermitian Chern Insulators, Physical Review Research 3, 023001 (2021)
We investigate the Hall conductance of a two-dimensional 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 non-Hermitian topology in fermionic transport experiments.
Ayukaryana, Nur R. and Fauzi, Mohammad H. and Hasdeo, Eddwi H., The Quest and Hope of Majorana Zero Modes in Topological Superconductor for Fault-Tolerant 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 anti-particle. Owing to its non-Abelian exchange statistics, Majorana fermions may act as a qubit for a universal quantum computer which is fault-tolerant. The existence of such particle is predicted in mid-gap 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 non-Abelian anyons on various platforms of certain Majorana fermion signature encountered.
Wu, Kunmin and Schmidt, Thomas L. and Farias, M. Belén, Quantum Friction in the Hydrodynamic Model, arXiv:2012.10204 [quant-ph] (2020)
We study the phenomenon of quantum friction in a system consisting of a polarizable atom moving at a constant speed parallel to a metallic plate. The metal is described using a charged hydrodynamic model for the electrons. This model featuring long-range interactions is appropriate for a clean metal in a temperature range where scattering due to Coulomb interactions dominates over the scattering of electron by impurities. We find that a quantum friction force between the atom and the metal surface exists even in the absence of intrinsic damping in the metal, but that it only starts once the velocity of the atom exceeds the effective speed of sound in the metal. We argue that this condition can be fulfilled most easily in metals with nearly empty or nearly filled bands. We make quantitative predictions for the friction force to the second and fourth order in the atomic polarizability, and show that the threshold behavior persists to all orders of the perturbation theory.
Rendy, Bernardus and Hasdeo, Eddwi H., Strain Effects on Band Structure and Dirac Nodal-Line Morphology of ZrSiSe, J. Appl. Phys. 129, 014306 (2020)
The Dirac nodal-line semimetals (DNLS) are new promising materials for technological applications due to its exotic properties, which originate from band structures dispersion and nodal-line behavior. We report a study on effects of several possibilities of strains in ZrSiSe DNLS on band structure dispersion and nodal-line behavior through the means of the density functional theory (DFT) calculations. We found that the Dirac nodal-line 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 nodal-line and band structures are equi-biaxial tensile, uniaxial (100) tensile, and uniaxial (110) tensile strain.
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 weak-coupling 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.
Michelsen, Andreas B. and Schmidt, Thomas L. and Idrisov, Edvin G., Current Correlations of Cooper-Pair Tunneling into a Quantum Hall System, Phys. Rev. B 102, 125402 (2020)
We study Cooper-pair 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 finite-frequency 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.
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.
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 Bi-Doped CaMnO3 for Thermoelectric Applications, arXiv:2001.08443 [cond-mat.mes-hall] (2020)
Electron and phonon transports in CaMnO3 and its Bi-doped counterpart, Bi0.03Ca0.97MnO3, are investigated by thermoelectric transport measurements, Raman spectroscopy, and first-principles calculations. In particular, we focus on CaMnO3 and Bi0.03Ca0.97MnO3's electronic structures, temperature-dependent electron and phonon lifetimes, and their sound velocities. We find that the anti-ferromagnetic insulator CaMnO3 breaks the Wiedemann-Franz (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.
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 electron-electron interactions. Compared to Majorana bound states, they offer richer non-Abelian 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 one-dimensional systems. We present the necessary theoretical tools for their study, in particular bosonization and the renormalization-group technique, and show how those can be applied to study parafermions.
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 fault-tolerant 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. Single-electron tunneling and processes involving creation and annihilation of Cooper pairs dominate in the sequential-tunneling 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 four-terminal 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.
Tschirhart, Hugo and Ong, Ernest T. S. and Sengupta, Pinaki and Schmidt, Thomas L., Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction, Phys. Rev. B 100, 195111 (2019)
We investigate an antiferromagnetic spin-1 Heisenberg chain in the presence of Dyzaloshinskii-Moriya 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 spin-1 chain on a spin-1/2 ladder and using a bosonization approach.
Idrisov, Edvin G. and Schmidt, Thomas L., Entropy production in one-dimensional quantum fluids, Phys. Rev. B 100, 165404 (2019)
We study nonequilibrium thermodynamic properties of a driven one-dimensional 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 three-particle collisions, and we derive its scaling law at low temperatures.
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 one-dimensional quantum fluid, Phys. Rev. Lett. 123, 075302 (2019)
We study a one-dimensional 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 finite-frequency 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.
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 non-Abelian 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.
Kristof Moors and Thomas L. Schmidt and Oleksiy Kashuba, Supersonic flow and negative local resistance in hydrodynamic Dirac electron nozzles, arXiv:1905.01247 [cond-mat.mes-hall] (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.
Moors, Kristof and Zyuzin, Alexander A. and Zyuzin, Alexander Yu. and Tiwari, Rakesh P. and Schmidt, Thomas L., Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals, Phys. Rev. B 99, 041116 (2019)
We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy 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 disorder-induced 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 non-Hermitian topological phases of matter.
Calzona, Alessio and Gambetta, Filippo Maria and Carrega, Matteo and Cavaliere, Fabio and Schmidt, Thomas L. and Sassetti, Maura, Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature, SciPost Phys. 4, 023 (2018)
It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law $∝ t^-2$ in its long-time 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 non-equilibrium fermionic spectral function are considered. We show that the non-universal 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 long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour.
Alessio Calzona and Tobias Meng and Maura Sassetti and Thomas L. Schmidt, Z4 parafermions in one-dimensional 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 spin-1/2 fermions which preserves the locality of operators with Z4 symmetry. Based on this mapping, we construct an exactly solvable, local, and interacting one-dimensional fermionic Hamiltonian which hosts zero-energy 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.
Wolf, Sebastian and Schmidt, Thomas L. and Rachel, Stephan, Unconventional superconductivity in the extended Hubbard model: Weak-coupling renormalization group, Phys. Rev. B 98, 174515 (2018)
We employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Repulsive interactions usually lead to higher-angular momentum Cooper pairing. By considering not only longer-ranged hoppings, but also nonlocal electron-electron 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 band-structure 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.
Groenendijk, Solofo and Dolcetto, Giacomo and Schmidt, Thomas L., Fundamental limits to helical edge conductivity due to spin-phonon scattering, Phys. Rev. B 97, 241406 (2018)
We study the effect of electron-phonon interactions on the electrical conductance of a helical edge state of a two-dimensional 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 spin-phonon 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 Bloch-Grüneisen law. At temperatures on the order of the Debye temperature of the host material, spin-phonon 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 finite-temperature conductivity of a helical edge channel.
Moors, Kristof and Schüffelgen, Peter and Rosenbach, Daniel and Schmitt, Tobias and Schäpers, Thomas and Schmidt, Thomas L., Magnetotransport signatures of three-dimensional 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 Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field, and the spin-momentum 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 half-integer magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A right-angle kink shows a unique $π$-periodic magnetoconductance signature as a function of the in-plane angle of the magnetic field. For a Y-junction, 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.
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 strong-coupling regime, Phys. Rev. B 97, 205405 (2018)
We establish a theoretical method which goes beyond the weak-coupling 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 system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band 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 Coulomb-coupled 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 weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.
Haughian, Patrick and Esposito, Massimiliano and Schmidt, Thomas L., Quantum thermodynamics of the resonant-level model with driven system-bath coupling, Phys. Rev. B 97, 085435 (2018)
We study nonequilibrium thermodynamics in a fermionic resonant-level model with arbitrary coupling strength to a fermionic bath, taking the wide-band 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.
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 Franck-Condon blockade. Here, we investigate this effect in a quantum dot driven by time-periodic gate voltages and tunneling amplitudes using nonequilibrium Green's functions and a Floquet expansion. Building on previous results showing that driving can lift the Franck-Condon 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.
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)
Two-particle backscattering in time-reversal 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 proximity-induced 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 time-reversal symmetry breaking, which causes the two-particle backscattering to be a sub-leading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.
Acciai, Matteo and Calzona, Alessio and Dolcetto, Giacomo and Schmidt, Thomas L. and Sassetti, Maura, Charge and energy fractionalization mechanism in one-dimensional channels, Phys. Rev. B 96, 075144 (2017)
We study the problem of injecting single electrons into interacting one-dimensional 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 energy-resolved electron. Our results shed light on how fractionalization occurs via the creation of particle-hole 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 spin-Hall edge states.
Kornich, Viktoriia and Pedder, Christopher J. and Schmidt, Thomas L., Spin-orbit coupling in quasi-one-dimensional Wigner crystals, Phys. Rev. B 95, 045413 (2017)
We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D 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 low-energy 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.
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 side-coupled 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.
Christoph P. Orth and Tibor Sekera and Christoph Bruder and Thomas L. Schmidt, The topological Anderson insulator phase in the Kane-Mele 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 Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele 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 lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.
Dolcetto, Giacomo and Sassetti, Maura and Schmidt, Thomas L., Edge physics in two-dimensional 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 two-dimensional topological insulators whose one-dimensional edge states are characterized by spin-momentum locking and protected by time-reversal 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 one-dimensional world called helical Luttinger liquid, whose theoretical properties and experimental observations are reviewed.
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 spin-orbit 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 spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional 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 sine-Gordon model. For special interaction strengths, we verify our results by re-fermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.
Haughian, Patrick and Walter, Stefan and Nunnenkamp, Andreas and Schmidt, Thomas L., Lifting the Franck-Condon blockade in driven quantum dots, Phys. Rev. B 94, 205412 (2016)
Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electron-vibron coupling strength. Here, we investigate the effect of a time-dependent 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 Born-Markov 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.
Schmidt, Thomas L. and Pedder, Christopher J., Helical gaps in interacting Rashba wires at low electron densities, Phys. Rev. B 94, 125420 (2016)
Rashba spin-orbit 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 one-dimensional 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.
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 single-electron sources in integer quantum Hall systems has paved the way for exploring electronic quantum optics experiments in solid-state devices. In this paper, we characterize a single Kramers pair emitter realized by a driven antidot embedded in a two-dimensional topological insulator, where spin-momentum 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 two-electron state. We study the concurrence C of the emitted state and the efficiency F of its emission as a function of the different spin-preserving and spin-flipping 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 Clauser-Horne-Shimony-Holt inequality.
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 two-dimensional topological insulator. We focus on the most generic and experimentally relevant case with broken axial spin symmetry. Spin-nonconservation 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 tight-binding simulation. We then extend this model by including Coulomb repulsion on the antidot, and we study the transport in the Coulomb-blockade limit. We investigate sequential tunneling and cotunneling regimes, and we find that the current-voltage characteristic allows a spectroscopic measurement of the edge-state spin textures.
Christoph P. Orth and Rakesh P. Tiwari and Tobias Meng and Thomas L. Schmidt, Non-Abelian parafermions in time-reversal invariant interacting helical systems, Phys. Rev. B 91, 081406(R) (2015)
The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional 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 time-reversal invariant. We determine the zero-energy 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 time-reversal 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.
Chris J. Pedder and Tobias Meng and Rakesh P. Tiwari and Thomas L. Schmidt, $8π$-periodic Josephson effect in time-reversal invariant interacting Rashba nanowires, arXiv:1507.08881 [cond-mat.mes-hall] (2015)
We investigate narrow quantum wires with strong Rashba spin-orbit coupling and electron-electron 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 time-reversal symmetry. Using the superconducting proximity effect to gap out the remaining modes, we show that the system can host zero-energy states at its edges, which are protected by time-reversal symmetry. We present the parameter regime in which these bound states will emerge. Similarly to Majorana bound states, they will produce a zero-bias 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 $e/2$.
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 higher-order current correlations for a modified Hanbury Brown-Twiss interferometer, we note that the cumulant-generating function can be interpreted such that unit-charge transfer processes correspond to two independent half-charge transfer processes, or alternatively, to two independent electron-hole 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.
Chao, Sung-Po and Schmidt, Thomas L. and Chung, Chung-Hou, 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 single-point 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 single-point contact.
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 two-dimensional topological insulator with broken axial spin symmetry. By considering honeycomb and square-lattice realizations of topological insulators, we show that in all cases the generic behavior of a momentum-dependent 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 spin-quantization 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 spin-quantization axis of the helical edge states.
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 Bardeen-Cooper-Schrieffer 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.
Gangadharaiah, Suhas and Schmidt, Thomas L. and Loss, Daniel, Structure factor of interacting one-dimensional 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 single-particle 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 mobile-impurity analysis reveals power-law singularities in $S(q,ømega)$ which depend on the interaction strength as well as on the spin texture of the edge states. For $|μ|
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.
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 T-shaped 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 cross-correlation 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 tight-binding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the cross-correlation functions.
Nussbaum, Jennifer and Schmidt, Thomas L. and Bruder, Christoph and Tiwari, Rakesh P., Josephson effect in normal and ferromagnetic topological-insulator junctions: Planar, step, and edge geometries, Phys. Rev. B 90, 045413 (2014)
We investigate Josephson junctions on the surface of a three-dimensional 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 spin-momentum 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 out-of-plane 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.
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 single-qubit gate. Supplemented with one braiding operation, this gate allows us to perform arbitrary single-qubit operations.
Thomas L. Schmidt, Finite-temperature conductance of interacting quantum wires with Rashba spin-orbit coupling, Phys. Rev. B 88, 235429 (2013)
We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($μ=0$), two-particle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $|μ| > 0$, three-particle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear single-particle 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.
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 two-dimensional topological insulator, which are connected by one or several local tunnel junctions. In the presence of spatially inhomogeneous Rashba spin-orbit 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.
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 single-electron 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 low-frequency ac transport, the charge-relaxation resistance (Rq) is a nontrivial function of the parameters of the system. However, in the vicinity of the charge-degeneracy points and for weak tunneling, we find as a result of cross-mode 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 one-channel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of near-perfect transmission using a bosonization approach. Focusing on the two-channel case, we study the effect of backscattering at the lead-dot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weak-tunneling regime near the charge-degeneracy points.
Schmidt, Thomas L. and Nunnenkamp, Andreas and Bruder, Christoph, Microwave-controlled coupling of Majorana bound states, New J. Phys. 15, 025043 (2013)
We propose microwave-controlled 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 single-qubit control necessary for universal quantum computation with Majorana qubits.
Walter, Stefan and Trauzettel, Björn and Schmidt, Thomas L., Transport properties of double quantum dots with electron-phonon 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 electron-phonon 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.
Imambekov, Adilet and Schmidt, Thomas L. and Glazman, Leonid I., One-dimensional 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 one-dimensional (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 low-energy 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 Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size 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.
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 low-temperature conductance of a weakly interacting one-dimensional 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 temperature-dependent 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 Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence of Rashba spin-orbit coupling.
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 pair-correlation 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.
H. Mönig and R. Caballero and C.A. Kaufmann and T.L. Schmidt and M.Ch. Lux-Steiner 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 current-voltage ($I(U)$) 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 X-ray 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 non-oxidized sample.
S. Maier and T. L. Schmidt and A. Komnik, Charge transfer statistics of a molecular quantum dot with strong electron-phonon 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 Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon 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 strong-coupling regime.
Schmidt, Thomas L., Current Correlations in Quantum Spin Hall Insulators, Phys. Rev. Lett. 107, 096602 (2011)
We consider a four-terminal setup of a two-dimensional 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 electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the inter-edge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross-correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.
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 one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave 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.
Thomas L. Schmidt and Kjetil Børkje and Christoph Bruder and Björn Trauzettel, Detection of qubit-oscillator 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.
Thomas L. Schmidt and Adilet Imambekov and Leonid I. Glazman, Fate of 1D Spin-Charge 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 zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.
Thomas L. Schmidt and Adilet Imambekov and Leonid I. Glazman, Spin-charge separation in one-dimensional fermion systems beyond Luttinger liquid theory, Phys. Rev. B 82, 245104 (2010)
We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the power-law singularities of the spectral function and the charge- and spin-density 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 spin-charge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy.
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 single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon 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 low-energy 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.
V. Koerting and T. L. Schmidt and C. B. Doiron and B. Trauzettel and C. Bruder, Transport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillator, Phys. Rev. B 79, 134511 (2009)
We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair 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 linear-response regime, we discuss and compare results of higher-order 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.
Roman-Pascal 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 Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon 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 self-consistent time-dependent mean-field 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.
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 resonant-level 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 time-dependent nonlinear current-voltage 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.
T. L. Schmidt and A. Komnik and A. O. Gogolin, Hanbury Brown--Twiss 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 fixed-point correlations they provide a promising means for extracting information on the parameters of the underlying Fermi-liquid model from the experimental data.
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 spin-resolved 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 on-site 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 spin-up and -down polarized electron flows, which has the potential to become a powerful instrument for the investigation of the Kondo effect in nanostructures.
T. L. Schmidt and A. Komnik, Nonlinear transport through a dynamic impurity in a strongly interacting one-dimensional electron gas, Phys. Rev. B 76, 035113 (2007)
We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent 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 current-voltage 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.
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 spin-resolved 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.
T. L. Schmidt and A. Komnik, On the visibility of electron--electron 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 electron--electron 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 single-wall carbon nanotubes.