The Bogoliubov equations and their application to a normal-superconducting boundary
Mathews, Wesley Northey
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https://hdl.handle.net/2142/25053
Description
Title
The Bogoliubov equations and their application to a normal-superconducting boundary
Author(s)
Mathews, Wesley Northey
Issue Date
1966
Doctoral Committee Chair(s)
Bardeen, John
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Bogoliubov equations
normal-superconducting boundary
pair potential
electron excitations
Language
en
Abstract
The Bogo1iubov equations are used to investigate the pair
potential and the electronic excitations associated with a norma1-
superconducting boundary in an extreme type I superconductor,
The method of the Bogoliubov equations has three advantages,
for this calculation, over other methods: (1) the method offers a
practical means of investigating the properties of a norma1-
superconducting boundary for all temperatures below the transition
temperature; (2) much of the physical insight associated with sing1eparticle
wave functions can be brought to bear, and (3) the effects
of non1ocality in the electrodynamics are taken into account from the
outset.
The foundation for the calculation is laid by a derivation
and discussion of the Bogoliubov equations, in the course of which
the equations are extended over the entire range of coupling strengths,
Four il1ustrative examples are considered: (1) the BCS limit;
(2) the normal conductor-superconductor contact; (3) an isolated
vortex line in a type II superconductor, and (4) a superconductor
containing non-magnetic impurities near the transition temperature,
1
IIn
the discussion of the fourth example, the Ginzburg-Landau equations,
for arbitrary electronic mean free path, are derived. In addition,
the kernels of the Ginzburg-Landau theory are expressed in terms of
the wave vector and frequency-dependent, normal conductivity.
The Bogoliubov equations are then used to work out the
theory of the properties of the boundary. A method which bears an
external resemblance to the standard JWKB approximation of quantum
mechanics is utilized to solve the Bogoliubov equations. There is,
however, an important difference: the method is capable in principle
of giving exact results - the form of the eigenfunctions is not
approximated. With the use of the physical picture that these
solutions present local BCS states, and assuming all quantities to
vary slowly over atomic distances, but permitting appreciable variations
over the Ginzburg-Landau coherence distance, the theory of the
normal-superconducting boundary is worked out to lowest approximation.
Some typical numerical results for the eigenfunctions are given.
The possible improvements in and the logical extensions of
the investigation are discussed. This investigation should serve
as a starting point for a complete, microscopic calculation of the
fundamental properties of the intermediate state. Also, the method
of solution of the Bogoliubov equations should prove useful for a
wide variety of problems.
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