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

Kormanyos, Andor and Kaufmann, Z. and Cserti, J. and Lambert, Colin J. (2003) Logarithmic contribution to the density of states of rectangular Andreev billiards. Physical Review B: Condensed Matter, 67 (17). p. 172506. ISSN 1550-235X

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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.

Item Type: Journal Article
Journal or Publication Title: Physical Review B: Condensed Matter
Additional Information: ©2003 The American Physical Society
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qc
Departments: Faculty of Science and Technology > Physics
ID Code: 572
Deposited By: Prof Colin J. Lambert
Deposited On: 04 Jul 2007
Refereed?: Yes
Published?: Published
Last Modified: 25 Feb 2020 01:17
URI: https://eprints.lancs.ac.uk/id/eprint/572

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