Bound states in Andreev billiards with soft walls

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.

8 pages, 6 figures, submitted to Phys. Rev

References in corpus (5)

• Ballistic quantum transport at high energies and high magnetic fields
• Adiabatic quantization of Andreev levels
• Effective Random Matrix Theory description of chaotic Andreev billiards
• A logarithmic contribution to the density of states of rectangular Andreev billiards
• Andreev bound states for superconducting-ferromagnetic box

Cited by in corpus (4)

• Simulation of Electron Transport through a Quantum Dot with Soft Walls
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Graphene Andreev Billiards
• Decreasing excitation gap in Andreev billiards by disorder scattering