Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity
Adagideli, İnanc̜
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https://hdl.handle.net/2142/31305
Description
Title
Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity
Author(s)
Adagideli, İnanc̜
Issue Date
2001
Doctoral Committee Chair(s)
Goldbart, Paul M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
inhomogeneous superconductor
Andreev billiards
cuprate superconductors
Language
en
Abstract
Semiclassical approaches to inhomogeneous superconductivity are explored within
three settings. The first is that of Andreev billiards, which are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. A theoretical framework
for the investigation of the short-wave quantal properties of quasiparticles in
Andreev billiards is developed. Among the central results are two semiclassical trace
formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality; and (ii) Higher-resolution corrections, expressed as a sum over periodic orbits that creep around the billiard boundary. The second involves quasiparticle motion near an extended
impurity in a d-wave superconductor. Via an extension of the quasiclassical
approximation, the idea that sign-variations in the superconducting pair-potential
lead to low-energy states is extended beyond its original setting of boundary scattering
to the broader context of scattering by general single-particle potentials. The
index-theoretic origin of these states is exhibited via a connection with Witten's super-symmetric quantum-mechanical model. The third concerns an extended impurity in a
cuprate superconductor in the pseudogap regime. It is shown that if the d-wave correlations persist into the pseudogap regime, but with pair-potential phase-fluctuations that destroy long-range ordering, then the low-energy states near extended impurities in the superconducting state should persist as resonances in the pseudogap regime. Thus, such states can serve as a probe of d-wave correlations in the pseudogap regime.
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