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Bound states in Andreev billiards with soft walls

F. Libisch·S. Rotter·J. Burgdoerfer·A. Kormanyos·J. Cserti
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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 (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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F. Libisch, S. Rotter, J. Burgdoerfer, A. Kormanyos, J. Cserti. 2005-04-05. Bound states in Andreev billiards with soft walls. https://doi.org/10.1103/physrevb.72.075304

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