Logarithmic contribution to the density of states of rectangular Andreev billiards

A. Kormányos, Z. Kaufmann, J. Cserti, C. J. Lambert

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Article number172506
Pages (from-to)1725061-1725064
Number of pages4
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume67
Issue number17
Publication statusPublished - May 2003

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Sommerfeld approximation
Superconducting materials
Geometry
energy
geometry
predictions

ASJC Scopus subject areas

  • Condensed Matter Physics

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Logarithmic contribution to the density of states of rectangular Andreev billiards. / Kormányos, A.; Kaufmann, Z.; Cserti, J.; Lambert, C. J.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 67, No. 17, 172506, 05.2003, p. 1725061-1725064.

Research output: Contribution to journalArticle

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