Bound states in Andreev billiards with soft walls
Megjelenés dátuma: 2005
MTMT: 1205014
WoS ID: 000231564500091
Scopus ID: 33749159204
Absztrakt:
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.