The Bogoliubov equations and their application to a normal-superconducting boundary

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Mathews, Wesley Northey

Contributors dc:contributor

• Bardeen, John

• Bogoliubov equations
• normal-superconducting boundary
• pair potential
• electron excitations

Statement dc:rights

• Copyright 1966 Wesley Northey Mathews

Language dc:language

en

Identifier

6127693

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/25053