Bound states in Andreev billiards with soft walls
arXiv:cond-mat/0504098 · doi:10.1103/PhysRevB.72.075304
Abstract
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 solutions with a semiclassical analysis using a Bohr--Sommerfeld (BS) quantization of periodic orbits. We propose a simple extension of the BS approximation which is well suited to describe Andreev billiards with parabolic potential walls. The underlying classical periodic electron-hole orbits are directly identified in terms of ``scar'' like features engraved in the quantum wavefunctions of Andreev states determined here for the first time.
arXiv comment8 pages, 6 figures, submitted to Phys. Rev
References in corpus (22)
- Random-Matrix Theory of Quantum Transport
- Phase coherent transport in hybrid superconducting nanostructures
- Spectral Flow, Magnus Force and Mutual Friction via the Geometric Optics Limit of Andreev Reflection
- Re-entrance of the metallic conductance in a mesoscopic proximity superconductor
- Induced superconductivity distinguishes chaotic from integrable billiards
- Angle dependence of Andreev scattering at semiconductor-superconductor interfaces
- Chaos in Andreev Billiards
- Density of States and Energy Gap in Andreev Billiards
- Ballistic quantum transport at high energies and high magnetic fields
- Excitation spectrum of Andreev billiards with a mixed phase space
- Adiabatic quantization of Andreev levels
- Semiclassical theory of quasiparticles in the superconducting state
- Proximity-induced sub-gaps in Andreev billiards
- Effective Random Matrix Theory description of chaotic Andreev billiards
- Ring--Shaped Andreev Billiards in Quantizing Magnetic Fields
- Quantal Andreev billiards: Density of states oscillations and the spectrum-geometry relationship
- Excitation spectra for Andreev billiards of Box and Disk geometries
- A pseudointegrable Andreev billiard
- A logarithmic contribution to the density of states of rectangular Andreev billiards
- Andreev bound states for superconducting-ferromagnetic box
- Andreev bound states for cake shape superconducting-normal systems
- Negative length orbits in normal-superconductor billiard systems