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Title:  Effects of anisotropy of the superconducting energy gap 
Author(s):  Clem, John Richard 
Doctoral Committee Chair(s):  Bardeen, John; Kadanoff, L.P. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  anisotropy
superconducting energy gap thermodynamic properties singlecrystal superconductors BCS model 
Abstract:  Various effects of anisotropy of the superconducting energy gap are theoretically considered. In order to estimate the effects of anisotropy upon the thermodynamic properties of pure, singlecrystal superconductors, a factorable BCSlike model for the effective electronelectron matrix element Vp p • = [1 + a. (p) ] V [1 +a(p')] is used. The IN\ W\ effects of anisotropy upon the temperature dependence of the gap parameter 6p ' the critical field, and the specific heat near the critical temperature are shown to be small and proportional to the meansquared anisotropy < a2 ), which .is of the order of 0.02 for typical superconductors. A number of processes, such as those involved in lowtemperature specific heat, nuclear spinlattice re1axati9n time, tunneling, surface resistance, and longitudinal ultrasonic attenuation are more sensitive to the details of the anisotropy than are the above thermodynamic properties. Theoretical expressions which explicitly include the anisotropy of a general gap parameter are given for these processes. In order to simplify the description of these effects, two quantities, the anisotropy distribution function P(a) and the reduced, an~sotropic, effective density of states, are introduced. The influence of the presence of nonmagnetic impurities upon the anisotropy of the superconducting energy gap parameter is consideredo Using the above BeSlike model within the context of an earlier theory by Markowitz and Kadanoff, it is shown that when impurities are present the wavevectordependent gap parameter Ap is replaced by a complex, wavevectorand energydependent gap parameter A(p,(I) = VV\ A. «I) + a (p) Aa (CD) • ~ Vo.A The behavior of Ai(m) and Aa(ro} is extensively examined as a function of impurity concentration: it is found, for example, that the magnitude of the anisotropic part Aa(ro) of the gap parameter tends to zero in the limit of large impurity concentration. A model calculation, assuming a rectangular shape for the anisotropy distribution function p'(a) I illustrates the behavior for small and moderate impurity concentrations. The behavior for large impurity concentrations is found to depend, to lowest order, only upon < a2 >. The behavior of th~.effective density of states is also examined and is shown to become isotropic as the impurity concentration increases. The precise shape of the effective density of states for energies near the gap is obtained for the large impurity concentration limit. The experimental manifestations of the reduction of the anisotropy by impurity scattering are considered. The thermodynamic properties are discussed in terms of the behavior of quantities of the order of the meansquared anisotropy; the more sensitive experimental processes are discussed in terms of the impurity concentrationdependent behavior of the effective density of states. 
Issue Date:  1965 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/23968 
Rights Information:  Copyright 1965 John Richard Clem 
Date Available in IDEALS:  20110519 
Identifier in Online Catalog:  6196947 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois