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Proximity-Induced Subgaps in Andreev Billiard.

Research output: Contribution to journalJournal article

Published

Journal publication date2002
JournalPhysical Review Letters
Journal number5
Volume89
Pages057001
Original languageEnglish

Abstract

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semiclassical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semiclassical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.