Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Adagideli, İnanc̜

Contributors dc:contributor

• Goldbart, Paul M.

• inhomogeneous superconductor
• Andreev billiards
• cuprate superconductors

Statement dc:rights

• ©2001 İnanc̜ Adagideli

Language dc:language

en

Identifier

4549671

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31305