arXiv subjects

C. W. J. Beenakker

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

At least 73 records · Page 4Linked to original sources

arXiv2018

Valley switch in a graphene superlattice due to pseudo-Andreev reflection

Dirac electrons in graphene have a valley degree of freedom that is being explored as a carrier of information. In that context of "valleytronics" one seeks to coherently manipulate the valley index. Here we show that reflection from a superlattice potential can provide a valley switch: Electrons approaching a pristine-graphene--superlattice-graphene interface near normal incidence are reflected in the opposite valley. We identify the topological origin of this valley switch, by mapping the problem onto that of Andreev reflection from a topological superconductor, with the electron-hole degree of freedom playing the role of the valley index. The valley switch is ideal at a symmetry point of the superlattice potential, but remains close to 100% in a broad parameter range.

cond-mat.mes-hall↗

arXiv2018

Twisted Fermi surface of a thin-film Weyl semimetal

The Fermi surface of a conventional two-dimensional electron gas is equivalent to a circle, up to smooth deformations that preserve the orientation of the equi-energy contour. Here we show that a Weyl semimetal confined to a thin film with an in-plane magnetization and broken spatial inversion symmetry can have a topologically distinct Fermi surface that is twisted into a $\mbox{figure-8}$ $-$ opposite orientations are coupled at a crossing which is protected up to an exponentially small gap. The twisted spectral response to a perpendicular magnetic field $B$ is distinct from that of a deformed Fermi circle, because the two lobes of a \mbox{figure-8} cyclotron orbit give opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels come in two counterpropagating types, a wide channel of width $βl_m^2\propto 1/B$ and a narrow channel of width $l_m\propto 1/\sqrt B$ (with $l_m=\sqrt{\hbar/eB}$ the magnetic length and $β$ the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.

cond-mat.mes-hall↗

arXiv2018

Machine-learning-assisted correction of correlated qubit errors in a topological code

A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.

quant-ph↗

arXiv2017

Adaptive weight estimator for quantum error correction

Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from a physical model of the error processes that affect the qubits. This approach becomes problematic if the system has sources of error that change over time. Here we show how the weights can be determined from the measured data in the absence of an error model. The resulting adaptive decoder performs well in a time-dependent environment, provided that the characteristic time scale $τ_{\mathrm{env}}$ of the variations is greater than $δt/\bar{p}$, with $δt$ the duration of one error-correction cycle and $\bar{p}$ the typical error probability per qubit in one cycle.

quant-ph↗

arXiv2017

Random-Matrix Theory of Quantum Size Effects on Nuclear Magnetic Resonance in Metal Particles

The distribution function of the local density of states is computed exactly for the Wigner-Dyson ensemble of random Hamiltonians. In the absence of time-reversal symmetry, precise agreement is obtained with the "supersymmetry" theory by Efetov and Prigodin of the NMR lineshape in disordered metal particles. Upon breaking time-reversal symmetry, the variance of the Knight shift in the smallest particles is reduced by a universal factor of 2/3. ***To be published in Physical Review B.****

cond-mat↗

arXiv2017

Andreev Reflection In Ferromagnet-Superconductor Junctions

The transport properties of a ferromagnet-superconductor (FS) junction are studied in a scattering formulation. Andreev reflection at the FS interface is strongly affected by the exchange interaction in the ferromagnet. The conductance G_FS of a ballistic point contact between F and S can be both larger or smaller than the value G_FN with the superconductor in the normal state, depending on the ratio of the exchange and Fermi energies. If the ferromagnet contains a tunnel barrier (I), the conductance G_FIFS exhibits resonances which do not vanish in linear response -- in contrast to the Tomasch oscillations for non-ferromagnetic materials.

cond-mat↗

arXiv2017

Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which diffuse in a $ d $-dimensional disordered metallic conductor of characteristic Thouless energy $ E_c. $ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $ f(\varepsilon ). $ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $ \varepsilon E_c, $ $ f(\varepsilon ) $ vanishes as a power law in $ \varepsilon /E_c $ with exponents $ -{1 \over 2},-2, $ and $ -{3 \over 2} $ for $ d=1,2, $ and 3, respectively. While for $ d=1,2 $ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion.

cond-mat↗

arXiv2017

Production and detection of three-qubit entanglement in the Fermi sea

Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how 3 qubits can be entangled without using electron-electron interactions. As in the 2-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium -- in contrast to the photonic analogue. The 3 qubits are represented by 4 edge-channel excitations in the quantum Hall effect (2 hole excitations plus 2 electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible 3-qubit entanglement is characterized by the tangle, which is expressed in terms of the transmission matrices of the tunneling point contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is obtained for channel-independent tunnel probabilities. We show how low-frequency noise measurements can be used to determine an upper and lower bound to the tangle. The bounds become tighter the closer the electron-hole state is to the GHZ state.

cond-mat.mes-hall↗

arXiv2017

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2λ_0 t})$ in the main part of phase space. The coefficient $λ_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-λ_1 t}$ is single exponential with a different coefficient $λ_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the classical limit $\hbar\to 0$ for times less than the Ehrenfest time $τ_E=\frac{1}{2}λ_0^{-1}|\ln \hbar|$. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.

nlin.CD↗

arXiv2017

Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit $\hbar\to 0$, which opens up a gap $E_{\rm gap}$ in the excitation spectrum. The time scale $\hbar/E_{\rm gap}\proptoα^{-1}\ln\hbar$ (with $α$ the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.

cond-mat.mes-hall↗

arXiv2017

Quantum teleportation by particle-hole annihilation in the Fermi sea

A tunnel barrier in a degenerate electron gas was recently discovered as a source of entangled particle-hole excitations. The entanglement is produced by elastic tunneling events, without requiring electron-electron interactions. Here we investigate the inverse process, the annihilation of an electron and a hole by elastic scattering. We find that this process leads to teleportation of the (unknown) state of the annihilated electron to a second, distant electron -- if the latter was previously entangled with the annihilated hole. We propose an experiment, involving low-frequency noise measurements on a two-dimensional electron gas in a high magnetic field, to detect teleportation of electrons and holes in the two lowest Landau levels.

cond-mat.mes-hall↗

arXiv2017

Electron-hole entanglement in the Fermi sea

I. Introduction (Preface, Exciton entanglers, Photon entanglers) II. Entanglement basics (Quantum versus classical correlations, Bell inequality, Entanglement measures for pure states, Entanglement measures for mixed states, Particle conservation, Phase reference) III. How to entangle free particles (Free bosons, Free fermions) IV. Spin versus orbital entanglement V. Entanglement detection by noise measurements (Tunneling regime, Beyond the tunneling regime, Full counting statistics) VI. Loss of entanglement by dephasing VII. Quantum entanglement pump VIII. Teleportation by electron-hole annihilation IX. Three-qubit entanglement X. The experimental challenge

cond-mat.mes-hall↗

arXiv2017

Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

Recent experiments by Gutiérrez $\textit{et al.}$ [Nature Phys. $\textbf{12}$, 950 (2016)] on a graphene-copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice --- a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called "Kek-Y" texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field $B$ the valley degeneracy of the $B$-dependent Landau levels is removed by the valley-momentum locking --- but a $B$-independent and valley-degenerate zero-mode remains.

cond-mat.mes-hall↗

arXiv2017

Chirality blockade of Andreev reflection in a magnetic Weyl semimetal

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

cond-mat.mes-hall↗

arXiv2017

Superconductivity provides access to the chiral magnetic effect of an unpaired Weyl cone

The massless fermions of a Weyl semimetal come in two species of opposite chirality, in two cones of the band structure. As a consequence, the current $j$ induced in one Weyl cone by a magnetic field $B$ (the chiral magnetic effect, CME) is cancelled in equilibrium by an opposite current in the other cone. Here we show that superconductivity offers a way to avoid this cancellation, by means of a flux bias that gaps out a Weyl cone jointly with its particle-hole conjugate. The remaining gapless Weyl cone and its particle-hole conjugate represent a single fermionic species, with renormalized charge $e^\ast$ and a single chirality $\pm$ set by the sign of the flux bias. As a consequence, the CME is no longer cancelled in equilibrium but appears as a supercurrent response $\partial j/\partial B=\pm(e^\ast e/h^2)μ$ along the magnetic field at chemical potential $μ$.

cond-mat.mes-hall↗

arXiv2016

Weyl-Majorana solenoid

A Weyl semimetal wire with an axial magnetization has metallic surface states (Fermi arcs) winding along its perimeter, connecting bulk Weyl cones of opposite topological charge (Berry curvature). We investigate what happens to this "Weyl solenoid" if the wire is covered with a superconductor, by determining the dispersion relation of the surface modes propagating along the wire. Coupling to the superconductor breaks up the Fermi arc into a pair of Majorana modes, separated by an energy gap. Upon variation of the coupling strength along the wire there is a gap inversion that traps the Majorana fermions.

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↗

arXiv2016

Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface

$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $Φ$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/Φ$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $\propto 1/\sqrtΦ$ when the magnetic length $l_m=\sqrt{\hbar/eB}$ drops below the separation $L$ of the NS interfaces. The crossover to the slow decay of the critical current is accompanied by the appearance of a 2D array of current vortices and antivortices in the normal region, which form a bipartite rectangular lattice with lattice constant $\simeq l_m^2/L$. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.

cond-mat.supr-con↗