arXiv subjects

Thomas L. Schmidt

Publications and source records attributed to Thomas L. Schmidt.

At least 55 records · Page 3Linked to original sources

arXiv2021

Magnetotransport signatures of three-dimensional topological insulator nanostructures

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.

cond-mat.mes-hall↗

arXiv2021

Generalized Chern numbers based on open system Green's functions

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 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 over the damping are made. Away from these conditions, which cannot or are not usually considered within the formalism of non-Hermitian 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.

cond-mat.mes-hall↗

arXiv2020

Quantum friction in the Hydrodynamic Model

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.

quant-ph↗

arXiv2020

Electron hydrodynamics of anomalous Hall materials

We study two-dimensional 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 two-dimensional infinite geometry, the Berry curvature leads to current whirlpools and an asymmetry of potential profile. This phenomenon can be probed by measuring the asymmetric non-local resistance profile.

cond-mat.mes-hall↗

arXiv2020

Universal Hall conductance scaling in non-Hermitian Chern insulators

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 non-analytical 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 electronic transport experiments.

cond-mat.mes-hall↗

arXiv2020

Heat transport in overdamped quantum systems

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 time scale separation associated with the overdamped regime, and without assuming the usual weak coupling and Markovian approximations. We find that non-trivial quantum corrections survive even when the temperatures are high compared to the frequency scale relevant for the overdamped dynamics of the system.

quant-ph↗

arXiv2020

Current correlations of Cooper-pair tunneling into a quantum Hall system

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 tunnelling 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 case of tunnelling into a single edge channel both the conductance and differential shot noise vanish as a result of Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a non-zero conductance and shot noise are revealed.

cond-mat.mes-hall↗

arXiv2020

Casimir force between Weyl semimetals in a chiral medium

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, and for realistic experimental parameters its magnitude can be greatly enhanced at short distances of a few microns 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.

cond-mat.mes-hall↗

arXiv2020

Parafermion braiding in fractional quantum Hall edge states with finite chemical potential

Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $\mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states 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.

cond-mat.str-el↗

arXiv2019

Transport properties of Majorana bound states networks in the Coulomb blockade regime

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 network 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.

cond-mat.mes-hall↗

arXiv2019

Bosonization for fermions and parafermions

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.

cond-mat.mes-hall↗

arXiv2019

Entropy production in one-dimensional quantum fluids

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.

cond-mat.mes-hall↗

arXiv2019

Phase diagram of spin-$1$ chains with Dzyaloshinskii-Moriya interaction

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.

cond-mat.str-el↗

arXiv2019

Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

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.

cond-mat.mes-hall↗

arXiv2018

Unconventional superconductivity in the extended Hubbard model: Weak-coupling renormalization group

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 non-local 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 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.

cond-mat.supr-con↗

arXiv2018

Z4 parafermions in one-dimensional fermionic lattices

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 $\mathbb{Z}_4$ parafermions and lattice spin-$1/2$ fermions which preserves the locality of operators with $\mathbb{Z}_4$ 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.

cond-mat.str-el↗

arXiv2018

Mechanical resonances of mobile impurities in a one-dimensional quantum fluid

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.

cond-mat.quant-gas↗

arXiv2018

Fundamental limits to helical edge conductivity due to spin-phonon scattering

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 lowers the conductivity of the edge state drastically. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $δG \propto T^5$ 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.

cond-mat.mes-hall↗