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

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Logarithmic contribution to the density of states of rectangular Andreev billiards. / Kormanyos, Andor; Kaufmann, Z.; Cserti, J. et al.
In: Physical Review B: Condensed Matter, Vol. 67, No. 17, 15.05.2003, p. 172506.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Kormanyos, A, Kaufmann, Z, Cserti, J & Lambert, CJ 2003, 'Logarithmic contribution to the density of states of rectangular Andreev billiards.', Physical Review B: Condensed Matter, vol. 67, no. 17, pp. 172506. https://doi.org/10.1103/PhysRevB.67.172506

APA

Vancouver

Kormanyos A, Kaufmann Z, Cserti J, Lambert CJ. Logarithmic contribution to the density of states of rectangular Andreev billiards. Physical Review B: Condensed Matter. 2003 May 15;67(17):172506. doi: 10.1103/PhysRevB.67.172506

Author

Kormanyos, Andor ; Kaufmann, Z. ; Cserti, J. et al. / Logarithmic contribution to the density of states of rectangular Andreev billiards. In: Physical Review B: Condensed Matter. 2003 ; Vol. 67, No. 17. pp. 172506.

Bibtex

@article{f5ad3322ce624e079933e48026318bd5,
title = "Logarithmic contribution to the density of states of rectangular Andreev billiards.",
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.",
author = "Andor Kormanyos and Z. Kaufmann and J. Cserti and Lambert, {Colin J.}",
note = " {\textcopyright}2003 The American Physical Society",
year = "2003",
month = may,
day = "15",
doi = "10.1103/PhysRevB.67.172506",
language = "English",
volume = "67",
pages = "172506",
journal = "Physical Review B: Condensed Matter",
issn = "1550-235X",
publisher = "AMER PHYSICAL SOC",
number = "17",

}

RIS

TY - JOUR

T1 - Logarithmic contribution to the density of states of rectangular Andreev billiards.

AU - Kormanyos, Andor

AU - Kaufmann, Z.

AU - Cserti, J.

AU - Lambert, Colin J.

N1 - ©2003 The American Physical Society

PY - 2003/5/15

Y1 - 2003/5/15

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevB.67.172506

DO - 10.1103/PhysRevB.67.172506

M3 - Journal article

VL - 67

SP - 172506

JO - Physical Review B: Condensed Matter

JF - Physical Review B: Condensed Matter

SN - 1550-235X

IS - 17

ER -