Bound states in Andreev billiards with soft walls
F. Libisch, S. Rotter, J. Burgdörfer, A. Kormányos, J. Cserti
DOI 10.1103/PhysRevB.72.075304 · Physical Review B
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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.
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