Effects of anisotropy of the superconducting energy gap

Clem, John Richard

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https://hdl.handle.net/2142/23968 Copy

Description

Title

Effects of anisotropy of the superconducting energy gap

Author(s)

Clem, John Richard

Issue Date

1965

Doctoral Committee Chair(s)

• Bardeen, John
• Kadanoff, L.P.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• anisotropy
• superconducting energy gap
• thermodynamic properties
• single-crystal superconductors
• BCS model

Language

en

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, single-crystal superconductors, a factorable BCSlike model for the effective electron-electron 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 mean-squared 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 spin-lattice 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 non-magnetic impurities upon the anisotropy of the superconducting energy gap parameter is consideredo Using the above BeS-like 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 energy-dependent 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 mean-squared anisotropy; the more sensitive experimental processes are discussed in terms of the impurity concentration-dependent behavior of the effective density of states.

Type of Resource

text

Permalink

http://hdl.handle.net/2142/23968

Copyright and License Information

Copyright 1965 John Richard Clem

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