Decreasing excitation gap in Andreev billiards by disorder scattering

TL;DR

This paper numerically studies disordered Andreev billiards and finds that increasing disorder decreases the excitation gap, contrary to conventional expectations, by analyzing the eigenvalue spectrum of the Wigner-Smith time delay matrix.

Contribution

It reveals that the longest Wigner-Smith delay time, not the mean, governs the excitation gap in disordered Andreev billiards, challenging previous assumptions.

Findings

Disorder reduces the excitation gap in Andreev billiards.

The longest delay time increases with disorder, decreasing the gap.

Contradicts conventional predictions about the effect of disorder.

Abstract

We investigate the distribution of the lowest-lying energy states in a disordered Andreev billiard by solving the Bogoliubov-de Gennes equation numerically. Contrary to conventional predictions we find a decrease rather than an increase of the excitation gap relative to its clean ballistic limit. We relate this finding to the eigenvalue spectrum of the Wigner-Smith time delay matrix between successive Andreev reflections. We show that the longest rather than the mean time delay determines the size of the excitation gap. With increasing disorder strength the values of the longest delay times increase, thereby, in turn, reducing the excitation gap.