Related papers: Entanglement Distribution Statistic in Andreev Bil…
We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry (TRS). The scattered state of two incident…
A new type of classical billiard - the Andreev billiard - is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards,…
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance,…
The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an Andreev billiard semiclassically where the…
Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting energy gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the…
This is a review of recent advances in our understanding of how Andreev reflection at a superconductor modifies the excitation spectrum of a quantum dot. The emphasis is on two-dimensional impurity-free structures in which the classical…
An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the…
We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cut-off in the path length distribution $P(s)$ will possess an energy gap on the scale of the Thouless energy. An exact quantum…
A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric…
We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to $M$ conducting modes…
Recently semiclassical approximations have been successfully applied to study the effect of a superconducting lead on the density of states and conductance in ballistic billiards. However, the summation over classical trajectories involved…
We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding insight into…
The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N…
Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the…
The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the context of superconducting-normal hybrid…
The production of orbitally entangled electrons in quantum-chaotic dots is investigated from a statistical point of view. The degree of entanglement is quantified through the concurrence and the entanglement of formation. We calculate the…
We studied the energy levels of graphene based Andreev billiards consisting of a superconductor region on top of a monolayer graphene sheet. For the case of Andreev retro-reflection we show that the graphene based Andreev billiard can be…
We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the…
In a previous contribution (H.J. Stoeckmann, J. Phys. A35, 5165 (2002)), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the…
We present numerical results for the local density of states in semiclassical Andreev billiards. We show that the energy gap near the Fermi energy develops in a chaotic billiard. Using the same method no gap is found in similar square and…