Topics in theory of superconductivity

This thesis contains three independent parts on three different topics in theory of superconductivity. In the first part a theory of nonlocal electrodynamics of unconventional superconductors is developed and applied to calculate the magnetic penetration depth in the Meissner state for a simple d-wave model of the cuprate high temperature superconductors. We find that in the clean limit, contrary to the general belief, below a certain crossover temperature, the temperature dependence of the penetration depth is quadratic and not linear. The interplay between nonlocal effects on one hand and impurities, surface quality of the sample and crystal axes orientation on the other hand is discussed in detail. Also, a simple experiment to test the viability of our theory is proposed. In the second part a new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based entirely on the wave function formulation of the theory of weakly coupled superconductors. We find that, under certain conditions, both the local density of states and the free energy of an inhomogeneous superconductor can be expressed in terms of the resolvent of a supersymmetric Hamiltonian corresponding to an effective one-dimensional Schrodinger like equation, resolvent which obeys the so-called Gelfand-Dikii equation. These results are used to formulate general conditions under which the free energy can be evaluated analytically and to derive a gradient expansion of the free energy at arbitrary temperatures. Finally, in the third part we study a new class of superconducting mesoscopic devices, known as Andreev billiards, which consist of a normal region surrounded by a superconducting region. The classical mechanics of Andreev billiards is investigated by employing the tangent map technique, and general conditions under which these systems become chaotic are formulated and demonstrated. Also, the issue of the feasibility of certain experimental realizations of these systems is addressed.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Kosztin, Ioan

Contributors dc:contributor

• Leggett, Anthony J.

• superconductivity
• cuprate superconductors
• inhomogeneous superconductor
• Andreev billiards

Statement dc:rights

• ©1997 Kosztin

Language dc:language

en

Identifier

4052599

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30702