Flux Flow Conductivity of a Dirty Type-II Superconductor: Linear Response Theory with the Gor'kov-Eliashberg Singularity Taken into Account

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概要

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• The theories of Caroli and Maki, Thompson, and others on the flux flow conductivity of a dirty type-II superconductor near the upper critical field H_c_2 are incomplete in the d.c. limit. In these theories they have expanded the conductivity in powers of the order parameter Δ and calculated the second-order terms of the expansion. However, the higher-order terms are divergent in the d.c. limit, as first disscussed by Gor'kov and Eliashberg. In this paper we have calculated the conductivity taking into account this GE singularity in terms of linear response theory. We have set up integral equations for anomalous vertices representing this singularity with the accuracy to order <∣Δ_0∣^2> without restrictiong to the gapless limit, where <∣Δ_0∣^2> is the spatial average of the Abrikosov solution Δ_0 squared. Great simplifications have resulted due to the linear response approximation. When the spatially uniform electric field is expressed by a vector potential, no singularity occurs in effect and the result of simple perturbation theory to second order is justified. In the scalar potential gauge we must treat the singularity. The integral equations were solved in the d.c. limit and the conductivity, which is formally expressed as a divergent series, has turned out finite and has agreed with the result of the simple perturbation theory, which is also equal to the result in the vector potential gauge, within the limit of the approximation, i.e.,to order <∣Δ_0∣^2>. The theory satisfies gauge-invariance. The calculations of previous authors in the scalar potential gauge have been shown to be incorrect and been corrected. The approximations made by Gor'kov and Eliashberg which simplified their theory greatly, have been shown not to be good.

• 理論物理学刊行会の論文
• 1974-06-25

著者

• Imai Syozo

  Research Institute Of Electrical Communication Tohoku University

• Imai Syozo

  Research Institute Electrical Communication Tohoku University

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