We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip graphene (length L, width W, no impurities or defects) to obtain conductance and shot noise as a function Fermi energy. find that minimum conductivity order e2/h at point (when electron hole excitations are degenerate) is associated with maximum Fano factor (the ratio power mean current). For short wide strips equals 1/3, 3 times smaller than for Poisson process. This same value...

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations HgTe quantum wells. It is combination random potential and quadratic corrections proportional to p^2 sigma_z Dirac Hamiltonian can drive ordinary band insulator topological (having inverted gap). calculate location boundary at weak disorder show it corresponds crossing edge rather than mobility edge. Our mechanism for formation Anderson...

We numerically calculate the conductivity $\sigma$ of an undoped graphene sheet (size $L$) in limit vanishingly small lattice constant. demonstrate one-parameter scaling for random impurity scattering and determine function $\beta(\sigma)=d\ln\sigma/d\ln L$. Contrary to a recent prediction, flow has no fixed point ($\beta>0$) conductivities up beyond symplectic metal-insulator transition. Instead, data supports alternative which at Dirac increases logarithmically with sample size absence...

The Goos-H\"anchen (GH) effect is an interference on total internal reflection at interface, resulting in a shift $\ensuremath{\sigma}$ of the reflected beam along interface. We show that GH $p\mathrm{\text{\ensuremath{-}}}n$ interface graphene depends pseudospin (sublattice) degree freedom massless Dirac fermions, and find sign change angle incidence ${\ensuremath{\alpha}}^{*}=\mathrm{arcsin}\sqrt{\mathrm{sin}{\ensuremath{\alpha}}_{c}}$ determined by critical ${\ensuremath{\alpha}}_{c}$ for...

Vortices in two-dimensional superconductors with broken time-reversal and spin-rotation symmetry can bind states at zero excitation energy. These so-called Majorana bound transform a thermal insulator into metal may be used to encode topologically protected qubits. We identify an alternative mechanism for the formation of states, akin way which Shockley are formed on surfaces: An electrostatic line defect have pair end points. The explains appearance vortex-free lattice models chiral p-wave...

We improve the test to show impossibility of a quantum theory based on real numbers by larger ratio complex-to-real bound Bell-type parameter. In contrast previous theoretical and experimental proposals requires three settings for parties <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math> xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math>, but also six middle party...

We construct a periodically time-dependent Hamiltonian with phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing second incommensurate driving frequency, so that we study effect one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible perform experiments on 2D using cold atoms optical lattice.

In the semiclassical limit of open ballistic quantum systems, we demonstrate emergence instantaneous decay modes guided by classical escape faster than Ehrenfest time. The time associated quasibound states is smaller flight. remaining long-lived obey random-matrix statistics, renormalized in compliance with recently proposed fractal Weyl law for systems [W.T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically a model system, kicked rotator.

Abstract It is argued that the electron stripes as found in correlated oxides have to do with an unrecognized form of order. The manifestation this order robust property charge are at same time antiphase boundaries spin system. We demonstrate quantity which ordering sublattice parity, referring geometrie a bipartite lattice it can be subdivided two sublattices different ways. Reinterpreting standard results one-dimensional physics, we responsible for phenomenon spin-charge separation...

We have studied numerically the mesoscopic fluctuations of conductance a graphene strip (width W larger than length L), in an ensemble samples with different realizations random electrostatic potential landscape. For strong disorder (potential comparable to hopping energy), variance approximates value predicted by Altshuler-Lee-Stone theory universal fluctuations, Var GUCF=0.12 (W/L)(2e2/h)2. weaker is greatly enhanced if smooth on scale atomic separation. There no enhancement varies scale,...

We calculate the conductance G of a bipolar junction in graphene nanoribbon, high-magnetic field regime where Hall p-doped and n-doped regions is 2e^2/h. In absence intervalley scattering, result G=(e^2/h)(1-cos Phi) depends only on angle Phi between valley isospins (= Bloch vectors representing spinor polarization) at two opposite edges. This plateau versus Fermi energy insensitive to electrostatic disorder, while it destabilized by dispersionless edge state which may exist zigzag boundary....

We adapt a finite difference method of solution the two-dimensional massless Dirac equation, developed in context lattice gauge theory, to calculation electrical conduction graphene sheet or on surface topological insulator. The discretized equation retains single point (no ``fermion doubling''), avoids intervalley scattering as well trigonal warping, and preserves single-valley time-reversal symmetry $(=\text{symplectic}\text{ }\text{symmetry})$ at all length scales energies---at expense...

A Weyl semimetal with broken time-reversal symmetry has a minimum of two species fermions, distinguished by their opposite chirality, in pair cones at momenta $\pm K$ that are displaced the direction magnetization. Andreev reflection interface between normal state (N) and superconductor (S) pairs must involve switch otherwise it is blocked. We show this "chirality blockade" suppresses superconducting proximity effect when magnetization lies plane NS interface. Zeeman field can provide...

Abstract Most superconductors are thermal insulators. A disordered chiral p -wave superconductor, however, can make a transition to metal phase. Because heat is then transported by Majorana fermions, this phase referred as metal. Here we present numerical evidence that the mechanism for with increasing electrostatic disorder percolation of boundaries separating domains different Chern number. We construct network domain walls using spectral localizer “topological landscape function”, and...

It is known that fluctuations in the electrostatic potential allow for metallic conduction (nonzero conductivity limit of an infinite system) if carriers form a single species massless two-dimensional Dirac fermions. A nonzero uniform mass $\overline{M}$ opens up excitation gap, localizing all states at point charge neutrality. Here we investigate numerically whether $\ensuremath{\delta}M⪢\overline{M}\ensuremath{\ne}0$ can have similar effect as fluctuations, allowing point. Our negative...

This is a numerical study of quasiparticle localization in symmetry class \textit{BD} (realized, for example, chiral \textit{p}-wave superconductors), by means staggered-fermion lattice model two-dimensional Dirac fermions with random mass. For sufficiently weak disorder, the system size dependence average (thermal) conductivity $\sigma$ well described an effective mass $M_{\rm eff}$, dependent on first two moments $M(\bm{r})$. The vanishes linearly when $\bar{M}\to 0$, reproducing known...

We study the effect of electrostatic disorder on conductivity a three-dimensional antiferromagnetic insulator (a stack quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where increase first causes appearance surface conduction (via topological transition), followed by bulk metal-insulator transition). conducting states are stabilized an effective time-reversal symmetry that is broken locally but restored long length scales. A simple...

We formulate a linear response theory of the chiral magnetic effect in finite Weyl semimetal, expressing electrical current density $j$ induced by slowly oscillating field $B$ or chemical potential $\mu$ terms scattering matrix fermions at Fermi level. Surface conduction can be neglected infinite-system limit for $\delta j/\delta \mu$, but not B$: The chirally circulating surface arcs give comparable contribution to bulk cones no matter how large system is, because their smaller number is...

Abstract We demonstrate an implementation of the precise test dimension on qubit, using public IBM quantum computer, determinant witness. The accuracy is below 10 −3 comparing to maximal possible value witness in higher dimension. involving minimal independent sets preparation and measurement operations (gates) applied both for specific configurations parametric ones. robust against nonidealities such as incoherent leakage erroneous gate execution. Two devices failed by more than 5 standard...

Andreev reflection at a superconductor and Klein tunneling through an n-p junction in graphene are two processes that couple electrons to holes -- the former superconducting pair potential Delta latter electrostatic U. We derive energy spectra systems identical, low energies E<<Delta for antisymmetric profile U(-x,y)=-U(x,y). This correspondence implies bipolar junctions may have zero density of states Fermi level carry current equilibrium, analogously Josephson junctions. It also...

Dirac electrons in graphene have a valley degree of freedom that is being explored as carrier information. In context "valleytronics" one seeks to coherently manipulate the index. Here we show reflection from superlattice potential can provide switch: Electrons approaching pristine-graphene--superlattice-graphene interface near normal incidence are reflected opposite valley. We identify topological origin this switch, by mapping problem onto Andreev superconductor, with electron-hole playing...

Abstract Methods to discretize the Hamiltonian of a topological insulator or superconductor, without giving up on protection massless excitations (respectively, Dirac fermions Majorana fermions) are reviewed. The method tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent propagate dimensional space‐time lattice with dispersion: in dimensionless units. They avoid fermion doubling artefact that will spoil protection, while preserving...

We use the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two point contacts electron reservoirs. By calculating system-size-over-wave-length dependence of shot noise power we study crossover from wave particle dynamics. Both fully mechanical and semiclassical calculation are presented. find numerically both approaches that is reduced exponentially with ratio Ehrenfest time dwell time, agreement analytical predictions.

We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. show that group structure bulk Hamiltonians defects is exponentially extended when this additional condition met examine some its physical consequences. Those localization–delocalization transitions between phases with same boundary conductance as well gapless stabilized by