arXiv subjects

B. Béri

Publications and source records attributed to B. Béri.

At least 19 recordsLinked to original sources

arXiv2020

Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes

We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between resilience against coherent $X$- and $Z$-rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into three distinct classes, each resulting in qualitatively distinct final-state distributions. In particular, we show that a graph class exists where the logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold. In these classes, therefore, the logical level noise above the error-correction threshold can retain significant amount of coherence even for large-distance codes. To perform our analysis, we develop a Majorana-fermion representation of planar-graph surface codes and describe the characterization of logical-state storage using fermion-linear-optics-based simulations. We thereby generalize the approach introduced for the square lattice by Bravyi \textit{et al}. [npj Quantum Inf. 4, 55 (2018)] to surface codes on general planar graphs.

quant-ph↗

arXiv2019

Exact nonequilibrium transport in the topological Kondo effect

A leading candidate for experimental confirmation of the non-local quantum dynamics of Majorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function, and fractional charge quantisation observable via the Fano factor. In the universal regime, our results apply for generic anisotropy and even away from the Kondo limit as long as the system supports an emergent topological Kondo fixed point. Our approach thus provides key new qualitative insights and exact expressions for quantitative comparisons to future experimental data.

cond-mat.mes-hall↗

arXiv2018

Screening cloud and non-Fermi-liquid scattering in topological Kondo devices

The topological Kondo effect arises when conduction electrons in metallic leads are coupled to a mesoscopic superconducting island with Majorana fermions. Working with its minimal setup, we study the lead electron local tunneling density of states in its thermally smeared form motivated by scanning tunneling microscopy, focusing on the component $ρ_{2 k_F}$ oscillating at twice the Fermi wavenumber. As a function of temperature $T$ and at zero bias, we find that the amplitude of $ρ_{2 k_F}$ is nonmonotonic, whereby with decreasing $T$ an exponential thermal-length-controlled increase, potentially through an intermediate Kondo logarithm, crosses over to a $T^{1/3}$ decay. The Kondo logarithm is present only for tip-junction distances sufficiently smaller than the Kondo length, thus providing information on the Kondo screening cloud. The low temperature decay indicates non-Fermi-liquid scattering, in particular the complete suppression of single-particle scattering at the topological Kondo fixed point. For temperatures much below the Kondo temperature, we find that the $ρ_{2 k_F}$ amplitude can be described as a universal scaling function indicative of strong correlations. In a more general context, our considerations point towards the utility of $ρ_{2 k_F}$ in studying quantum impurity systems, including extracting information about the single-particle scattering matrix.

cond-mat.mes-hall↗

arXiv2018

Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal-invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical and numerical results that hold for arbitrary normal-state conductance and the most general forms of spin-orbit coupling. The signatures of topological superconductivity we find include the fractional ac Josephson effect, which arises in topological-topological junctions provided that the energy relaxation is sufficiently slow. We also show, for both junction types, that robust signatures of topological superconductivity arise in the dc Josephson effect in the form of switches in the Josephson current due to zero-energy crossings of Andreev levels. The junction spin-orbit coupling enters the Josephson current only in the topological-topological case and in a manner determined by the switch locations, thereby allowing quantitative predictions for experiments with the normal-state conductance, the induced gaps, and the switch locations as inputs.

cond-mat.mes-hall↗

arXiv2016

Random-matrix theory of thermal conduction in superconducting quantum dots

We calculate the probability distribution of the transmission eigenvalues T_n of Bogoliubov quasiparticles at the Fermi level in an ensemble of chaotic Andreev quantum dots. The four Altland-Zirnbauer symmetry classes (determined by the presence or absence of time-reversal and spin-rotation symmetry) give rise to four circular ensembles of scattering matrices. We determine P({T_n}) for each ensemble, characterized by two symmetry indices βand γ. For a single d-fold degenerate transmission channel we thus obtain the distribution P(g) ~ g^{-1+β/2}(1-g)^{γ/2} of the thermal conductance g (in units of d π^2 k_B^2 T_0/6h at low temperatures T_0). We show how this single-channel limit can be reached using a topological insulator or superconductor, without running into the problem of fermion doubling.

cond-mat.mes-hall↗

arXiv2012

Majorana-Klein hybridization in topological superconductor junctions

We present a powerful and general approach to describe the coupling of Majorana fermions to external leads, of interacting or non-interacting electrons. Our picture has the Klein factors of bosonization appearing as extra Majoranas hybridizing with the physical ones. We demonstrate the power of this approach by solving a highly nontrivial SO(M) Kondo problem arising in topological superconductors with M Majorana-lead couplings, allowing for arbitrary M and for conduction electron interactions. We find that these topological Kondo problems give rise to robust non-Fermi liquid behavior, even for Fermi liquid leads, and to a quantum phase transition between insulating and Kondo regimes when the leads form Luttinger liquids. In particular, for M=4 we find a long sought-after stable realization of the two-channel Kondo fixed point.

cond-mat.mes-hall↗

arXiv2012

Topological Kondo effect with Majorana fermions

The Kondo effect is a striking consequence of the coupling of itinerant electrons to a quantum spin with degenerate energy levels. While degeneracies are commonly thought to arise from symmetries or fine-tuning of parameters, the recent emergence of Majorana fermions has brought to the fore an entirely different possibility: a "topological degeneracy" which arises from the nonlocal character of Majorana fermions. Here we show that nonlocal quantum spins formed from these degrees of freedom give rise to a novel "topological Kondo effect". This leads to a robust non-Fermi liquid behavior, known to be difficult to achieve in the conventional Kondo context. Focusing on mesoscopic superconductor devices, we predict several unique transport signatures of this Kondo effect, which would demonstrate the non-local quantum dynamics of Majorana fermions, and validate their potential for topological quantum computation.

cond-mat.mes-hall↗

arXiv2012

Thermal metal-insulator transition in a helical topological superconductor

Two-dimensional superconductors with time-reversal symmetry have a Z_2 topological invariant, that distinguishes phases with and without helical Majorana edge states. We study the topological phase transition in a class-DIII network model, and show that it is associated with a metal-insulator transition for the thermal conductance of the helical superconductor. The localization length diverges at the transition with critical exponent nu approx 2.0, about twice the known value in a chiral superconductor.

cond-mat.mes-hall↗

arXiv2011

Z_2 Topological Insulators in Ultracold Atomic Gases

We describe how optical dressing can be used to generate bandstructures for ultracold atoms with non-trivial Z_2 topological order. Time reversal symmetry is preserved by simple conditions on the optical fields. We first show how to construct optical lattices that give rise to Z_2 topological insulators in two dimensions. We then describe a general method for the construction of three-dimensional Z_2 topological insulators. A central feature of our approach is a new way to understand Z_2 topological insulators starting from the nearly-free electron limit.

cond-mat.quant-gas↗

arXiv2011

Probing fractional topological insulators with magnetic edge perturbations

We discuss detection strategies for fractional topological insulators (FTIs) realizing time-reversal invariant analogues of fractional quantum Hall systems in the Laughlin universality class. Focusing on transport measurements, we study the effect of magnetic perturbations on the edge modes. We find that the modes show unexpected robustness against magnetic backscattering for moderate couplings and edge interactions, allowing for various phase transitions signaling the FTI phase. We also describe protocols for extracting the universal integer m characterizing the phase and the edge interaction parameter from the conductance of setups with magnets and a quantum point contact.

cond-mat.mes-hall↗

arXiv2011

Nonlocal conductance reveals helical superconductors

Helical superconductors form a two dimensional, time-reversal invariant topological phase characterized by a Kramers pair of Majorana edge modes (helical Majorana modes). Existing detection schemes to identify this phase rely either on spin transport properties, which are quite difficult to measure, or on local charge transport, which allows only a partial identification. Here we show that the presence of helical Majorana modes can be unambiguously revealed by measuring the nonlocal charge conductance. Focusing on a superconducting ring, we suggest two experiments that provide unique and robust signatures to detect the helical superconductor phase.

cond-mat.supr-con↗

arXiv2011

Local tensor network for strongly correlated projective states

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous efforts, strongly correlated projective states, fractional quantum Hall states in particular, have not yet found a local tensor network representation. Here we show that one can encode the calculation of averages of local operators in a Grassmann tensor network which is local. Our construction is explicit, and allows the use of physically motivated trial wavefunctions as starting points in tensor network variational calculations.

cond-mat.str-el↗

arXiv2010

Topologically stable gapless phases of time-reversal invariant superconductors

We show that time-reversal invariant superconductors in d=2 (d=3) dimensions can support topologically stable Fermi points (lines), characterized by an integer topological charge. Combining this with the momentum space symmetries present, we prove analogs of the fermion doubling theorem: for d=2 lattice models admitting a spin X electron-hole structure, the number of Fermi points is a multiple of four, while for d=3, Fermi lines come in pairs. We show two implications of our findings for topological superconductors in d=3: first, we relate the bulk topological invariant to a topological number for the surface Fermi points in the form of an index theorem. Second, we show that the existence of topologically stable Fermi lines results in extended gapless regions in a generic topological superconductor phase diagram.

cond-mat.supr-con↗

arXiv2009

Dephasing-enabled triplet Andreev conductance

We study the conductance of normal-superconducting quantum dots with strong spin-orbit scattering, coupled to a source reservoir using a single-mode spin-filtering quantum point contact. The choice of the system is guided by the aim to study triplet Andreev reflection without relying on half metallic materials with specific interface properties. Focusing on the zero temperature, zero-bias regime, we show how dephasing due to the presence of a voltage probe enables the conductance, which vanishes in the quantum limit, to take nonzero values. Concentrating on chaotic quantum dots, we obtain the full distribution of the conductance as a function of the dephasing rate. As dephasing gradually lifts the conductance from zero, the dependence of the conductance fluctuations on the dephasing rate is nonmonotonic. This is in contrast to chaotic quantum dots in usual transport situations, where dephasing monotonically suppresses the conductance fluctuations.

cond-mat.mes-hall↗

arXiv2009

Generalization of the Poisson kernel to the superconducting random-matrix ensembles

We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution generalizes the Poisson kernel to the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, our result cannot be obtained by combining the maximum entropy principle with the analyticity-ergodicity constraint. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.

cond-mat.mes-hall↗

arXiv2008

Quantum limit of the triplet proximity effect in half-metal - superconductor junctions

We apply the scattering matrix approach to the triplet proximity effect in superconductor-half metal structures. We find that for junctions that do not mix different orbital modes, the zero bias Andreev conductance vanishes, while the zero bias Josephson current is nonzero. We illustrate this finding on a ballistic half-metal--superconductor (HS) and superconductor -- half-metal -- superconductor (SHS) junction with translation invariance along the interfaces, and on HS and SHS systems where transport through the half-metallic region takes place through a single conducting channel. Our calculations for these physically single mode setups -- single mode point contacts and chaotic quantum dots with single mode contacts -- illustrate the main strength of the scattering matrix approach: it allows for studying systems in the quantum mechanical limit, which is inaccessible for quasiclassical Green's function methods, the main theoretical tool in previous works on the triplet proximity effect.

cond-mat.supr-con↗

arXiv2007

Splitting of Andreev levels in a Josephson junction by spin-orbit coupling

We consider the effect of spin-orbit coupling on the energy levels of a single-channel Josephson junction below the superconducting gap. We investigate quantitatively the level splitting arising from the combined effect of spin-orbit coupling and the time-reversal symmetry breaking by the phase difference between the superconductors. Using the scattering matrix approach we establish a simple connection between the quantum mechanical time delay matrix and the effective Hamiltonian for the level splitting. As an application we calculate the distribution of level splittings for an ensemble of chaotic Josephson junctions. The distribution falls off as a power law for large splittings, unlike the exponentially decaying splitting distribution given by the Wigner surmise -- which applies for normal chaotic quantum dots with spin-orbit coupling in the case that the time-reversal symmetry breaking is due to a magnetic field.

cond-mat.mes-hall↗

arXiv2006

Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

We consider the effect of spin-orbit coupling on the low energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor), using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: In zero magnetic field: (1) the narrowing of the distribution of the excitation gap; (2) the appearance of oscillations in the average density of states. In strong magnetic field: (3) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.

cond-mat.mes-hall↗