arXiv subjects

C. W. J. Beenakker

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

At least 145 records · Page 8Linked to original sources

arXiv2010

Geodesic scattering by surface deformations of a topological insulator

We consider the classical ballistic dynamics of massless electrons on the conducting surface of a three-dimensional topological insulator, influenced by random variations of the surface height. By solving the geodesic equation and the Boltzmann equation in the limit of shallow deformations, we obtain the scattering cross section and the conductivity σ, for arbitrary anisotropic dispersion relation. At large surface electron densities n this geodesic scattering mechanism (with σ propto sqrt{n}) is more effective at limiting the surface conductivity than electrostatic potential scattering.

cond-mat.mes-hall↗

arXiv2010

Flat-lens focusing of electrons on the surface of a topological insulator

We propose the implementation of an electronic Veselago lens on the conducting surface of a three-dimensional topological insulator (such as Bi2Te3). The negative refraction needed for such a flat lens results from the sign change of the curvature of the Fermi surface, changing from a circular to a snowflake-like shape across a sufficiently large electrostatic potential step. No interband transition (as in graphene) is needed. For this reason, and because the topological insulator provides protection against backscattering, the potential step is able to focus a broad range of incident angles. We calculate the quantum interference pattern produced by a point source, generalizing the analogous optical calculation to include the effect of a noncircular Fermi surface (having a nonzero conic constant).

cond-mat.mes-hall↗

arXiv2010

Effective mass and tricritical point for lattice fermions localized by a random mass

This is a numerical study of quasiparticle localization in symmetry class \textit{BD} (realized, for example, in chiral \textit{p}-wave superconductors), by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average (thermal) conductivity $σ$ is well described by an effective mass $M_{\rm eff}$, dependent on the first two moments of the random mass $M(\bm{r})$. The effective mass vanishes linearly when the average mass $\bar{M}\to 0$, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity $σ_{c}=1/π$ and critical exponent $ν=1$. For strong disorder a transition to a metallic phase appears, with larger $σ_{c}$ but the same $ν$. The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a \textit{repulsive} tricritical point.

cond-mat.mes-hall↗

arXiv2010

Absence of a metallic phase in charge-neutral graphene with a random gap

It is known that fluctuations in the electrostatic potential allow for metallic conduction (nonzero conductivity in the limit of an infinite system) if the carriers form a single species of massless two-dimensional Dirac fermions. A nonzero uniform mass $\bar{M}$ opens up an excitation gap, localizing all states at the Dirac point of charge neutrality. Here we investigate numerically whether fluctuations $δM \gg \bar{M} \neq 0$ in the mass can have a similar effect as potential fluctuations, allowing for metallic conduction at the Dirac point. Our negative conclusion confirms earlier expectations, but does not support the recently predicted metallic phase in a random-gap model of graphene.

cond-mat.mes-hall↗

arXiv2010

Nonzero temperature effects on antibunched photons emitted by a quantum point contact out of equilibrium

Electrical current fluctuations in a single-channel quantum point contact can produce photons (at frequency omega close to the applied voltage V x e/hbar) which inherit the sub-Poissonian statistics of the electrons. We extend the existing zero-temperature theory of the photostatistics to nonzero temperature T. The Fano factor F (the ratio of the variance and the average photocount) is <1 for T 1 for T>T_c (bunched photons). The crossover temperature T_c ~ Deltaomega x hbar/k_B is set by the band width Deltaomega of the detector, even if hbar x Deltaomega << eV. This implies that narrow-band detection of photon antibunching is hindered by thermal fluctuations even in the low-temperature regime where thermal electron noise is negligible relative to shot noise.

cond-mat.mes-hall↗

arXiv2009

Hartman effect and spin precession in graphene

Spin precession has been used to measure the transmission time τover a distance L in a graphene sheet. Since conduction electrons in graphene have an energy-independent velocity v, one would expect τ> L/v. Here we calculate that τ< L/v at the Dirac point (= charge neutrality point) in a clean graphene sheet, and we interpret this result as a manifestation of the Hartman effect (apparent superluminality) known from optics.

cond-mat.mes-hall↗

arXiv2009

Domain wall in a chiral p-wave superconductor: a pathway for electrical current

Superconductors with p+ip pairing symmetry are characterized by chiral edge states, but these are difficult to detect in equilibrium since the resulting magnetic field is screened by the Meissner effect. Nonequilibrium detection is hindered by the fact that the edge excitations are unpaired Majorana fermions, which cannot transport charge near the Fermi level. Here we show that the boundary between p_x+ip_y and p_x-ip_y domains forms a one-way channel for electrical charge. We derive a product rule for the domain wall conductance, which allows to cancel the effect of a tunnel barrier between metal electrodes and superconductor and provides a unique signature of topological superconductors in the chiral p-wave symmetry class.

cond-mat.supr-con↗

arXiv2009

Switching of electrical current by spin precession in the first Landau level of an inverted-gap semiconductor

We show how the quantum Hall effect in an inverted-gap semiconductor (with electron- and hole-like states at the conduction- and valence-band edges interchanged) can be used to inject, precess, and detect the electron spin along a one-dimensional pathway. The restriction of the electron motion to a single spatial dimension ensures that all electrons experience the same amount of precession in a parallel magnetic field, so that the full electrical current can be switched on and off. As an example, we calculate the magnetoconductance of a p-n interface in a HgTe quantum well and show how it can be used to measure the spin precession due to bulk inversion asymmetry.

cond-mat.mes-hall↗

arXiv2009

Theory of the topological Anderson insulator

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

cond-mat.mes-hall↗

arXiv2009

Pseudodiffusive transmission of nodal Dirac fermions through a clean d-wave superconductor

We calculate the transmission of electrons and holes between two normal-metal electrodes (N), separated over a distance L by an impurity-free superconductor (S) with d-wave symmetry of the order parameter. Nodal lines of vanishing excitation gap form ballistic conduction channels for coupled electron-hole excitations, described by an anisotropic two-dimensional Dirac equation. We find that the transmitted electrical and thermal currents, at zero energy, both have the pseudodiffusive 1/L scaling characteristic of massless Dirac fermions - regardless of the presence of tunnel barriers at the NS interfaces. Tunnel barriers reduce the slope of the 1/L scaling in the case of the electrical current, while leaving the thermal current unaffected.

cond-mat.mes-hall↗

arXiv2009

Applications of random matrix theory to condensed matter and optical physics

This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in experiments on quantum wires, quantum dots, disordered wave guides, and chaotic resonators. Topics considered include universal conductance fluctuations, weak localization and coherent backscattering, sub-Poissonian shot noise and open transmission channels, non-Gaussian conductance and thermopower distributions, mesoscopic superconductivity, grey-body radiation, and chaotic laser cavities.

cond-mat.mes-hall↗

arXiv2009

Quantum Goos-Hanchen effect in graphene

The Goos-Hanchen (GH) effect is an interference effect on total internal reflection at an interface, resulting in a shift sigma of the reflected beam along the interface. We show that the GH effect at a p-n interface in graphene depends on the pseudospin (sublattice) degree of freedom of the massless Dirac fermions, and find a sign change of sigma at angle of incidence alpha*=arcsin[sin alpha_c]^1/2 determined by the critical angle alpha_c for total reflection. In an n-doped channel with p-doped boundaries the GH effect doubles the degeneracy of the lowest propagating mode, introducing a two-fold degeneracy on top of the usual spin and valley degeneracies. This can be observed as a stepwise increase by 8e^2/h of the conductance with increasing channel width.

cond-mat.mes-hall↗

arXiv2009

Electrically detected interferometry of Majorana fermions in a topological insulator

We show how a chiral Dirac fermion (a massless electron or hole) can be converted into a pair of neutral chiral Majorana fermions (a particle equal to its own antiparticle). These two types of fermions exist on the metallic surface of a topological insulator, respectively, at a magnetic domain wall and at a magnet-superconductor interface. Interferometry of Majorana fermions is a key operation in topological quantum computation, but the detection is problematic since these particles have no charge. The Dirac-Majorana converter enables electrical detection of the interferometric signal.

cond-mat.mes-hall↗

arXiv2009

Two-photon speckle as a probe of multi-dimensional entanglement

We calculate the statistical distribution P_2(I_2) of the speckle pattern produced by a photon pair current I_2 transmitted through a random medium, and compare with the single-photon speckle distribution P_1(I_1). We show that the purity Tr rho^2 of a two-photon density matrix rho can be directly extracted from the first two moments of P_1 and P_2. A one-to-one relationship is derived between P_1 and P_2 if the photon pair is in an M-dimensional entangled pure state. For M>>1 the single-photon speckle disappears, while the two-photon speckle acquires an exponential distribution. The exponential distribution transforms into a Gaussian if the quantum entanglement is degraded to a classical correlation of M>>1 two-photon states. Two-photon speckle can therefore discriminate between multi-dimensional quantum and classical correlations.

quant-ph↗

arXiv2009

Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum

Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal. While constructive interference of a scalar (spin-zero) wave produces a coherent backscattering peak, consisting of a doubling of the disorder-averaged reflected photon flux, the destructive interference caused by the Berry phase suppresses the reflected intensity at an angle which is related to the angle of incidence by time-reversal symmetry. We demonstrate this extinction of coherent backscattering by a numerical solution of Maxwell's equations and compare with analytical predictions from the Dirac equation.

cond-mat.mes-hall↗

arXiv2009

Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution

The recent realization of a "Levy glass" (a three-dimensional optical material with a Levy distribution of scattering lengths) has motivated us to analyze its one-dimensional analogue: A linear chain of barriers with independent spacings s that are Levy distributed: p(s)~1/s^(1+alpha) for s to infinity. The average spacing diverges for 0<alpha<1. A random walk along such a sparse chain is not a Levy walk because of the strong correlations of subsequent step sizes. We calculate all moments of conductance (or transmission), in the regime of incoherent sequential tunneling through the barriers. The average transmission from one barrier to a point at a distance L scales as L^(-alpha) ln L for 0<alpha<1. The corresponding electronic shot noise has a Fano factor (average noise power / average conductance) that approaches 1/3 very slowly, with 1/ln L corrections.

cond-mat.dis-nn↗

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↗

arXiv2008

Finite difference method for transport properties of massless Dirac fermions

We adapt a finite difference method of solution of the two-dimensional massless Dirac equation, developed in the context of lattice gauge theory, to the calculation of electrical conduction in a graphene sheet or on the surface of a topological insulator. The discretized Dirac equation retains a single Dirac point (no "fermion doubling"), avoids intervalley scattering as well as trigonal warping, and preserves the single-valley time reversal symmetry (= symplectic symmetry) at all length scales and energies -- at the expense of a nonlocal finite difference approximation of the differential operator. We demonstrate the symplectic symmetry by calculating the scaling of the conductivity with sample size, obtaining the logarithmic increase due to antilocalization. We also calculate the sample-to-sample conductance fluctuations as well as the shot noise power, and compare with analytical predictions.

cond-mat.mes-hall↗