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
Full text not available from this repository.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.