Skip to main content
Article thumbnail
Location of Repository

Logarithmic contribution to the density of states of rectangular Andreev billiards.

By Andor Kormanyos, Z. Kaufmann, J. Cserti and Colin J. Lambert

Abstract

We demonstrate that the exact quantum mechanical calculations are in good agreement with the semiclassical predictions for rectangular Andreev billiards, and therefore for a large number of open channels it is sufficient to investigate the Bohr-Sommerfeld approximation of the density of states . We present exact calculations of the classical path length distribution P(s), which is a nondifferentiable function of s, but whose integral is a smooth function with logarithmically dependent asymptotic behavior. Consequently, the density of states of rectangular Andreev billiards has two contributions on the scale of the Thouless energy: one which is well-known and is proportional to the energy, and the other which shows a logarithmic energy dependence. It is shown that the prefactors of both contributions depend on the geometry of the billiards but have universal limiting values when the width of the superconductor tends to zero

Year: 2003
OAI identifier: oai:eprints.lancs.ac.uk:572
Provided by: Lancaster E-Prints

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.