Bound states in Andreev billiards with soft walls

Details Bound states in Andreev billiards with soft walls Bound states in Andreev billiards with soft walls

2005-04-05

arxiv.org/abs/cond-mat/0504098v1

Phys. Rev. B 72, 075304 (2005).

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 6 figures, submitted to Phys. Rev

Scientific paper

10.1103/PhysRevB.72.075304

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.

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