Bound states in Andreev billiards with soft walls

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

Research output: Contribution to journalArticle

8 Citations (Scopus)


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
Issue number7
Publication statusPublished - Aug 15 2005

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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