Decreasing excitation gap in Andreev billiards by disorder scattering

¹  Institute for Theoretical Physics, Vienna University of Technology - A-1040 Vienna, Austria, EU
²  Department of Applied Physics, Yale University - New Haven, CT 06520, USA
³  Department of Physics, University of Wisconsin - Madison, WI 53706, USA

Corresponding author: florian@concord.itp.tuwien.ac.at

Received: 14 January 2008
Accepted: 27 March 2008

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.