Bound states in Andreev billiards with soft walls

F. Libisch, S. Rotter, J. Burgdörfer, A. Kormányos, J. Cserti

Research output: Article

8 Citations (Scopus)

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 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 wave functions of Andreev states which we determine here explicitly.

Original languageEnglish
Article number075304
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume72
Issue number7
DOIs
Publication statusPublished - aug. 15 2005

Fingerprint

Sommerfeld approximation
Orbits
orbits
scars
Wave functions
Superconducting materials
Semiconductor quantum dots
eigenvectors
energy spectra
quantum dots
wave functions
Electrons

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Bound states in Andreev billiards with soft walls. / Libisch, F.; Rotter, S.; Burgdörfer, J.; Kormányos, A.; Cserti, J.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 72, No. 7, 075304, 15.08.2005.

Research output: Article

Libisch, F. ; Rotter, S. ; Burgdörfer, J. ; Kormányos, A. ; Cserti, J. / Bound states in Andreev billiards with soft walls. In: Physical Review B - Condensed Matter and Materials Physics. 2005 ; Vol. 72, No. 7.
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