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Transformation of Gorkov's equation for type II superconductors into transport-like equations

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Zeitschrift für Physik A Hadrons and nuclei

Abstract

The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameterΔ(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially Lüders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations.

The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fieldsΔ andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations.

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Work supported in part by the Battelle Memorial Institute, Columbus, Ohio, USA.

Part of this work was done during a two years stay at the Physics Department, Cornell University, Ithaca, N.Y. I like to extend my warmest thanks to its faculty and staff members for the nice and stimulating time, I had with them. The work has been finished in the framework of a program for research on superconductivity, sponsored in part by the Battelle Memorial Institute, Columbus, Ohio, which is gratefully acknowledged. I have also benefitted from many discussions with Dr.Büttner of the Battelle Institute, Frankfurt a. Main, and I am indebted to Mr. P. K.Sarma for many valuable comments on the manuscript.

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Eilenberger, G. Transformation of Gorkov's equation for type II superconductors into transport-like equations. Z. Physik 214, 195–213 (1968). https://doi.org/10.1007/BF01379803

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  • DOI: https://doi.org/10.1007/BF01379803

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