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F. Libisch, J. Möller, S. Rotter, M.G. Vavilov, J. Burgdörfer:
"Decreasing excitation gap in Andreev billiards by disorder scattering.";
Poster: DPG Fruehjahrstagung, 2009, Dresden, Deutschland; 2009-03-23 - 2009-03-27.

We investigate the distribution of the lowest-lying energy states in
a disordered Andreev billiard by solving the Bogoliubov-de Gennes
equation numerically [1]. 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.

Andreev Billiards, Wigner-Smith time delay