Bound states in Andreev billiards with soft walls

Libisch, F. and Rotter, S. and Burgdörfer, J. and Kormanyos, Andor and Cserti, J. (2005) Bound states in Andreev billiards with soft walls. Physical review B, 72 (7). 075304. ISSN 1550-235X

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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.

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Journal Article
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Physical review B
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06 Jun 2008 15:32
Last Modified:
21 Nov 2022 20:50