Related papers: Proximity-induced sub-gaps in Andreev billiards
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…
When a quantum-chaotic normal conductor is coupled to a superconductor, random-matrix theory predicts that a gap opens up in the excitation spectrum which is of universal size $E_g^{\rm RMT}\approx 0.3 \hbar/t_D$, where $t_D$ is the mean…
The validity of the retracing approximation in the semiclassical quantization of Andreev billiards is investigated. The exact energy spectrum and the eigenstates of normal-conducting, ballistic quantum dots in contact with a superconductor…
The energy spectrum and the eigenstates of a rectangular quantum dot containing soft potential walls in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes (BdG) equation. We compare the quantum mechanical…
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much…
Energy spectra of a particle with mass $m$ and charge $e$ in the cubic Aharonov-Bohm billiard containing around $10^4$ consecutive levels starting from the ground state have been analysed. The cubic Aharonov-Bohm billiard is a plane…
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…
Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…
Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and…
In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy $E$ in the region outside the rectangular set in the high-energy limit. We use the adiabatic ansatz to compare the Dirichlet energy form…
An Andreev billiard was realized in an array of niobium filled antidots in a high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C of the Nb dots we observe a strong reduction of the resistance around B=0 and a…
We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to…
We study Andreev billiards of box and disk geometries by matching the wave functions at the interface of the normal and the superconducting region using the exact solutions of the Bogoliubov-de Gennes equation. The mismatch in the Fermi…
The arithmetic triangular billiards are classically chaotic but have Poissonian energy level statistics, in ostensible violation of the BGS conjecture. We show that the length spectra of their periodic orbits divides into subspectra…
We calculate the density P(\tau) of the eigenvalues of the Wigner-Smith time delay matrix for two-dimensional rectangular and circular billiards with one opening. For long times, the density of these so-called "proper delay times" decays…
We present a microscopic theory of the Andreev gap, i.e. the phenomenon that the density of states (DoS) of normal chaotic cavities attached to superconductors displays a hard gap centered around the Fermi energy. Our approach is based on a…
The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…
We construct semi-infinite billiard domains which reverse the direction of most incoming particles. We prove that almost all particles will leave the open billiard domain after a finite number of reflections. Moreover, with high probability…
We calculate the subgap density of states of a disordered single-channel normal metal connected to a superconductor at one end (NS junction) or at both ends (SNS junction). The probability distribution of the energy of a bound state…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…