arXiv subjects

C. W. J. Beenakker

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

At least 181 records · Page 10Linked to original sources

arXiv2007

Voltage-probe and imaginary potential models for dephasing in a chaotic quantum dot

We compare two widely used models for dephasing in a chaotic quantum dot: The introduction of a fictitious voltage probe into the scattering matrix and the addition of an imaginary potential to the Hamiltonian. We identify the limit in which the two models are equivalent and compute the distribution of the conductance in that limit. Our analysis explains why previous treatments of dephasing gave different results. The distribution remains non-Gaussian for strong dephasing if the coupling of the quantum dot to the electron reservoirs is via ballistic single-mode point contacts, but becomes Gaussian if the coupling is via tunneling contacts.

cond-mat↗

arXiv2007

Why does a metal-superconductor junction have a resistance?

This is a tutorial article based on a lecture delivered in June 1999 at the NATO Advanced Study Institute in Ankara. The phenomenon of Andreev reflection is introduced as the electronic analogue of optical phase-conjugation. In the optical problem, a disordered medium backed by a phase-conjugating mirror can become completely transparent. Yet, a disordered metal connected to a superconductor has the same resistance as in the normal state. The resolution of this paradox teaches us a fundamental difference between phase conjugation of light and electrons.

cond-mat.mes-hall↗

arXiv2007

Reentrance effect in a graphene n-p-n junction coupled to a superconductor

We study the interplay of Klein tunneling (= interband tunneling) between n-doped and p-doped regions in graphene and Andreev reflection (= electron-hole conversion) at a superconducting electrode. The tunneling conductance of an n-p-n junction initially increases upon lowering the temperature, while the coherence time of the electron-hole pairs is still less than their lifetime, but then drops back again when the coherence time exceeds the lifetime. This reentrance effect, known from diffusive conductors and ballistic quantum dots, provides a method to detect phase coherent Klein tunneling of electron-hole pairs.

cond-mat.mes-hall↗

arXiv2007

Hempel's dilemma and the physics of computation

Carl Gustav Hempel (1905-1997) formulated the dilemma that carries his name in an attempt to determine the boundaries of physics. Where does physics go over into metaphysics? The purpose of this contribution is to indicate how a recently developed field of research, the physics of computation, might offer a new answer to that old question: The boundary between physics and metaphysics is the boundary between what can and what cannot be computed in the age of the universe.

physics.hist-ph↗

arXiv2006

Detection of valley polarization in graphene by a superconducting contact

Because the valleys in the band structure of graphene are related by time-reversal symmetry, electrons from one valley are reflected as holes from the other valley at the junction with a superconductor. We show how this Andreev reflection can be used to detect the valley polarization of edge states produced by a magnetic field. In the absence of intervalley relaxation, the conductance G_NS=2(e^2/h)(1-cos(Theta)) of the junction on the lowest quantum Hall plateau is entirely determined by the angle Theta between the valley isospins of the edge states approaching and leaving the superconductor. If the superconductor covers a single edge, Theta=0 and no current can enter the superconductor. A measurement of G_NS then determines the intervalley relaxation time.

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↗

arXiv2006

Ballistic transmission through a graphene bilayer

We calculate the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length $L\ll$ width $W$), and compare with known results for a monolayer. At the Dirac point of charge neutrality, the bilayer transmits as two independent monolayers in parallel: Both current and noise are resonant at twice the monolayer value, so that their ratio (the Fano factor) has the same 1/3 value as in a monolayer -- and the same value as in a diffusive metal. The range of Fermi energies around the Dirac point within which this pseudo-diffusive result holds is smaller, however, in a bilayer than in a monolayer (by a factor $l_{\perp}/L$, with $l_{\perp}$ the interlayer coupling length).

cond-mat.mes-hall↗

arXiv2006

Degradation of electron-hole entanglement by spin-orbit coupling

Electron-hole pairs produced by tunneling in a degenerate electron gas lose their spin entanglement by spin-orbit coupling, which transforms the fully entangled Bell state into a partially entangled mixed density matrix of the electron and hole spins. We calculate the dependence of the entanglement (quantified by the concurrence) on the spin-orbit coupling time tau_so and on the diffusion time (or dwell time) tau_dwell of electron and hole in the conductors (with conductances >> e^2/h) at the two sides of the tunnel barrier (with conductance << e^2/h). The entanglement disappears when the ratio tau_dwell/tau_so exceeds a critical value of order unity. The results depend on the type of conductor (disordered wire or chaotic quantum dot), but they are independent of other microscopic parameters (number of channels, level spacing). Our analytical treatment relies on an "isotropy approximation" (no preferential basis in spin space), which allows us to express the concurrence entirely in terms of spin correlators. We test this approximation for the case of chaotic dynamics with a computer simulation (using the spin kicked rotator) and find good agreement.

cond-mat.mes-hall↗

arXiv2006

Pseudo-diffusive conduction at the Dirac point of a normal-superconductor junction in graphene

A ballistic strip of graphene (width W>> length L) connecting two normal metal contacts is known to have a minimum conductivity of 4e^{2}/pi h at the Dirac point of charge neutrality. We calculate what happens if one of the two contacts becomes superconducting. While the ballistic conductance away from the Dirac point is increased by Andreev reflection at the normal-superconductor (NS) interface, we find that the minimum conductivity stays the same. This is explained as a manifestation of pseudo-diffusive conduction at the Dirac point. As a generalization of our results for a ballistic system, we provide a relation between the conductance G_NS of an arbitrarily disordered normal-superconductor junction in graphene and its value G_N when both contacts are in the normal state.

cond-mat.mes-hall↗

arXiv2006

Excitation gap of a graphene channel with superconducting boundaries

We calculate the density of states of electron-hole excitations in a superconductor/normal-metal/superconductor (SNS) junction in graphene, in the long-junction regime that the superconducting gap is much larger than the Thouless energy. If the normal region is undoped, the excitation spectrum consists of neutral modes that propagate along the boundaries - transporting energy but no charge. These ``Andreev modes'' are a coherent superposition of electron states from the conduction band and hole states from the valence band, coupled by specular Andreev reflection at the superconductor. The lowest Andreev mode has an excitation gap, which depends on the superconducting phase difference across the SNS graphene channel. At high doping the excitation gap vanishes and the usual gapless density of states of Andreev levels is recovered. We use our results to calculate the superconducting phase dependence of the thermal conductance of the graphene channel.

cond-mat.mes-hall↗

arXiv2006

Valley filter and valley valve in graphene

It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled ``valley valve'', representing a zero-magnetic-field counterpart to the familiar spin valve.

cond-mat.mes-hall↗

arXiv2006

Three "universal" mesoscopic Josephson effects

1. Introduction 2. Supercurrent from Excitation Spectrum 3. Excitation Spectrum from Scattering Matrix 4. Short-Junction Limit 5. Universal Josephson Effects 5.1 Quantum Point Contact 5.2 Quantum Dot 5.3 Disordered Point Contact (Average supercurrent, Supercurrent fluctuations)

cond-mat.mes-hall↗

arXiv2006

Josephson effect in ballistic graphene

We solve the Dirac-Bogoliubov-De-Gennes equation in an impurity-free superconductor-normal-superconductor (SNS) junction, to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result is determined by the superconducting gap and by the aspect ratio of the junction (length L, small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result in which the Fermi wave length takes over from L. The product of critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.

cond-mat.mes-hall↗

arXiv2006

Specular Andreev reflection in graphene

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-De Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal--superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: 1) The electron and hole occupy different valleys of the band structure; 2) At normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wave lengths at the two sides of the interface; and, most fundamentally: 3) Away from normal incidence the reflection angle may be the same as the angle of incidence (retro-reflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wave length in the normal region is large compared to the superconducting coherence length. We find that the transition from retro-reflection to specular reflection with decreasing doping is associated with an inversion of the voltage dependence of the subgap conductance of the interface.

cond-mat.mes-hall↗

arXiv2006

Quantum Shot Noise

1. Types of electrical noise 2. Measuring the unit of transferred charge 3. Quiet electrons 4. Detecting open transmission channels 5. Distinguishing particles from waves 6. Entanglement detector

cond-mat.mes-hall↗

arXiv2006

Parity meter for charge qubits: an efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.

cond-mat.mes-hall↗

arXiv2006

Quantum-limited shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects), to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e^2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, three times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

cond-mat.mes-hall↗

arXiv2006

How spin-orbit interaction can cause electronic shot noise

The shot noise in the electrical current through a ballistic chaotic quantum dot with N-channel point contacts is suppressed for N --> infinity, because of the transition from stochastic scattering of quantum wave packets to deterministic dynamics of classical trajectories. The dynamics of the electron spin remains quantum mechanical in this transition, and can affect the electrical current via spin-orbit interaction. We explain how the role of the channel number N in determining the shot noise is taken over by the ratio l_{so}/lambda_F of spin precession length l_{so} and Fermi wave length lambda_F, and present computer simulations in a two-dimensional billiard geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of the shot noise in the regime lambda_F << l_{so} << W.

cond-mat.mes-hall↗