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https://hdl.handle.net/2142/30702
Description
Title
Topics in theory of superconductivity
Author(s)
Kosztin, Ioan
Issue Date
1997
Doctoral Committee Chair(s)
Leggett, Anthony J.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
superconductivity
cuprate superconductors
inhomogeneous superconductor
Andreev billiards
Language
en
Abstract
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.
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