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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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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.

Item Type: Article
Journal or Publication Title: Physical Review B
Uncontrolled Keywords: quantum dots ; mesoscopic systems ; quantum theory ; bound states ; electronic density of states
Subjects: Q Science > QC Physics
Departments: Faculty of Science and Technology > Physics
ID Code: 9408
Deposited By: Ms Margaret Calder
Deposited On: 06 Jun 2008 16:32
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 18:36
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/9408

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