Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -