arXiv subjects

C. W. J. Beenakker

Publications and source records attributed to C. W. J. Beenakker.

At least 37 records · Page 2Linked to original sources

arXiv2024

Chiral edge mode for single-cone Dirac fermions

We study the appearance of a chiral edge mode on the two-dimensional (2D) surface of a 3D topological insulator (TI). The edge mode appears along the 1D boundary with a magnetic insulator (MI), dependent on the angle $θ$ which the magnetization $M$ makes with the normal to surface and on the chemical potential mismatch $δμ$ across the TI--MI interface (assuming $1>δμ/M\equiv\sinϕ)$. The propagation along the interface is chiral, with velocity $v\cos(θ-ϕ)$ smaller than the Dirac fermion velocity $v$. In momentum space the edge mode is an arc state, extending over the finite momentum interval that connects the Dirac point of the gapless Dirac fermions with the magnetic band gap. An electric field parallel to the boundary pumps charge between TI and MI via this arc state.

cond-mat.mes-hall↗

arXiv2024

Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions

To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdotσ$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the \textit{nonlocal} Hamiltonian of tangent fermions permits a \textit{local} generalized eigenproblem.

cond-mat.str-el↗

arXiv2024

Josephson effect in a junction coupled to an electron reservoir

We extend the scattering theory of the Josephson effect to include a coupling of the Josephson junction to a gapless electron reservoir in the normal state. By opening up the system with a quasiparticle escape rate $1/τ$, the supercurrent carried at zero temperature by an Andreev level at energy $\varepsilon_{\rm A}$ is reduced by a factor $(2/π)\arctan(2\varepsilon_{\rm A}τ/\hbar)$ . We make contact with recent work on "non-Hermitian Josephson junctions", by comparing this result to different proposed generalizations of the Josephson effect to non-Hermitian Hamiltonians.

cond-mat.supr-con↗

arXiv2024

Topologically protected Casimir effect for lattice fermions

The electromagnetic Casimir effect has a fermionic counterpart in topological insulators: Zero-point fluctuations of a massless Dirac fermion field mediate a force between magnetic scatterers. The Casimir force is insensitive to disorder that preserves the topological protection of an unpaired Dirac cone. The protection may be broken if the Dirac equation is discretized, and an exponential suppression of the Casimir effect will result if a gap opens at the Dirac point. Here we show how this lattice artefact may be avoided, by applying a recently developed local discretization of the Euclidean action that does not suffer from the fermion-doubling obstruction of local discretizations of the Hamiltonian.

quant-ph↗

arXiv2023

Dynamical simulation of the injection of vortices into a Majorana edge mode

The chiral edge modes of a topological superconductor can transport fermionic quasiparticles, with Abelian exchange statistics, but they can also transport non-Abelian anyons: Edge-vortices bound to a $π$-phase domain wall that propagates along the boundary. A pair of such edge-vortices is injected by the application of an $h/2e$ flux bias over a Josephson junction. Existing descriptions of the injection process rely on the instantaneous scattering approximation of the adiabatic regime [Beenakker et al. Phys.Rev.Lett. 122, (2019)], where the internal dynamics of the Josephson junction is ignored. Here we go beyond that approximation in a time-dependent many-body simulation of the injection process, followed by a braiding of mobile edge-vortices with a pair of immobile Abrikosov vortices in the bulk of the superconductor. Our simulation sheds light on the properties of the Josephson junction needed for a successful implementation of a flying topological qubit.

cond-mat.mes-hall↗

arXiv2023

Casimir-Josephson force on a point contact between two superconductors

We calculate the elongation or contraction force $F$ on a point contact (length $L$) connecting two superconductors with a phase difference $ϕ$. When $L$ is small compared to the superconducting coherence length $ξ_0$ this force is given by $F=-(Δ_0/πξ_0)\ln(ξ_0/L)\cosϕ$ per spin-degenerate transverse mode. Quantum fluctuations in states from the continuous spectrum outside the superconducting gap $Δ_0$ give the dominant contribution to this force, which may be understood as the superconducting counterpart of the electromagnetic Casimir force. We compare with earlier work that only included contributions from the discrete spectrum of Andreev levels.

cond-mat.supr-con↗

arXiv2023

Phase-shifted Andreev levels in an altermagnet Josephson junction

We compute the effect of a d-wave magnetization (altermagnetism) on the spectrum of bound states (Andreev levels) in a junction between two s-wave superconductors (gap $Δ_0$, phase difference $ϕ$). Compared to a nonmagnetic junction, the $ϕ$-dependence of the spectrum is shifted by an offset $\pmδϕ$, dependent on the spin direction, so that the Andreev levels become spin-polarized. In a planar junction, oriented along the crystalline axis of $d_{xy}$-wave symmetry, the excitation energies are determined by the normal-state transmission probability $T$ according to $E=Δ_0\sqrt{1-T\sin^2\tfrac{1}{2}(ϕ\pmδϕ)}$. We calculate the corresponding Josephson energy and supercurrent, recovering the 0-$π$ transition of related studies.

cond-mat.supr-con↗

arXiv2023

Magnus effect on a Majorana zero-mode

A supercurrent on the proximitized surface of a topological insulator can cause a delocalization transition of a Majorana fermion bound to a vortex core as a zero-mode. Here we study the dynamics of the deconfinement, as a manifestation of the Magnus effect (the coupling of the superflow to the velocity field in the vortex). The initial acceleration of the Majorana fermion is $\pm 2v_{\rm F}^2 K/\hbar$, perpendicular to the Cooper pair momentum $K$, for a $\pm 2π$ winding of the superconducting phase around the vortex. The quasiparticle escapes with a constant velocity from the vortex core, which we calculate in a semiclassical approximation and compare with computer simulations.

cond-mat.mes-hall↗

arXiv2023

Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling

I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. Outlook

cond-mat.mes-hall↗

arXiv2023

Pair correlation function of the one-dimensional Riesz gas

A method from random-matrix theory is used to calculate the pair correlation function of a one-dimensional gas of $N\gg 1$ classical particles with a power law repulsive interaction potential $u(x)\propto |x|^{-s}$ (a socalled Riesz gas). An integral formula for the covariance of single-particle operators is obtained which generalizes known results in the limits $s\rightarrow -1$ (Coulomb gas) and $s\rightarrow 0$ (log-gas). As an application, we calculate the variance of the center of mass of the Riesz gas, which has a universal large-$N$ limit that does not depend on the shape of the confining potential.

cond-mat.stat-mech↗

arXiv2023

Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of "Wilson fermions", the chiral symmetry is broken and the zeroth Landau level is broadened when $B$ has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining $+B$ and $-B$ regions.

cond-mat.mes-hall↗

arXiv2022

Bloch oscillations in the magnetoconductance of twisted bilayer graphene

We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the bilayer maps onto an electric field. Bloch oscillations due to the periodic motion in a 1D Bloch band can then be observed in purely DC transport as magnetoconductance oscillations with periodicity set by the Bloch frequency.

cond-mat.mes-hall↗

arXiv2022

Breathing mode in open-orbit magnetotransport: a magnetic lens with a quantum mechanical focal length

We consider the propagation of electrons in a lattice with an anisotropic dispersion in the $x$--$y$ plane (lattice constant $a$), such that it supports open orbits along the $x$-axis in an out-of-plane magnetic field $B$. We show that a point source excites a "breathing mode", a state that periodically spreads out and refocuses after having propagated over a distance $\ell =(eaB/h)^{-1}$ in the $x$-direction. Unlike known magnetic focusing effects, governed by the classical cyclotron radius, this is an intrinsically quantum mechanical effect with a focal length $\propto\hbar$.

cond-mat.mes-hall↗

arXiv2022

Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone

The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. We show that this topological protection is absent in the familiar single-cone discretization with a linear sawtooth dispersion, as a consequence of the fact that there the time-evolution operator is discontinuous at Brillouin zone boundaries.

cond-mat.mes-hall↗

arXiv2022

Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation

Massless Dirac fermions in an electric field propagate along the field lines without backscattering, due to the combination of spin-momentum locking and spin conservation. This phenomenon, known as "Klein tunneling", may be lost if the Dirac equation is discretized in space and time, because of scattering between multiple Dirac cones in the Brillouin zone. To avoid this, a staggered space-time lattice discretization has been developed in the literature, with one single Dirac cone in the Brillouin zone of the original square lattice. Here we show that the staggering doubles the size of the Brillouin zone, which actually contains two Dirac cones. We find that this fermion doubling causes a spurious breakdown of Klein tunneling, which can be avoided by an alternative single-cone discretization scheme based on a split-operator approach.

cond-mat.mes-hall↗

arXiv2022

Supercell symmetry modified spectral statistics of Kramers-Weyl fermions

We calculate the spectral statistics of the Kramers-Weyl Hamiltonian $H=v\sum_α σ_α\sin p_α+t σ_0\sum_α\cos p_α$ in a chaotic quantum dot. The Hamiltonian has symplectic time-reversal symmetry ($H$ is invariant when spin $σ_α$ and momentum $p_α$ both change sign), and yet for small $t$ the level spacing distribution $P(s)\propto s^β$ follows the $β=1$ orthogonal ensemble instead of the $β=4$ symplectic ensemble. We identify a supercell symmetry of $H$ that explains this finding. The supercell symmetry is broken by the spin-independent hopping energy $\propto t\cos p$, which induces a transition from $β=1$ to $β=4$ statistics that shows up in the conductance as a transition from weak localization to weak antilocalization.

cond-mat.mes-hall↗

arXiv2021

Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}ψ=E {\mathcal P}ψ$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

cond-mat.mes-hall↗

arXiv2021

Chiral charge transfer along magnetic field lines in a Weyl superconductor

We identify a signature of chirality in the electrical conduction along magnetic vortices in a Weyl superconductor: The conductance depends on whether the magnetic field is parallel or antiparallel to the vector in the Brillouin zone that separates Weyl points of opposite chirality.

cond-mat.mes-hall↗