Fluctuation Conductivity and Vortex Flow Resistivity of a Dirty Strong-Coupling Superconductor

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Abstract
The theory of fluctuation conductivity of a dirty strong-coupling superconductor of Fulde and Maki based on an effective Hamiltonian which simulates retarded electron-electron interaction, is re-examined. It is found that their Hamiltonian violated causality and the arguments, by which they derived a time dependent Ginzburg-Landau (TDGL) equation contain difficulties. It seems that we cannot obtain TDGL equation in a simple form for a strong-coupling superconductor. In this paper we calculate fluctuation conductivity in terms of linear response theory without recourse to a TDGL equation by the phonon model of a superconductor. The fluctuation propagator of the order parameter becomes a function of two frequency variables which describes center-of-mass and relative motion, respectively, and satisfies an integral equation with respect to the latter frequency variable. These frequency dependence of the fluctuation propagator is discussed unambiguously, introducing a complete orthonormal set of eigenfunctions which diagonalize the fluctuation propagator. We have also discussed vortex flow resistivity near the upper critical field Hc2 of a dirty type-II strong-coupling superconductor. The absence of Meissner effect is shown rigorously, using the complete orthonormality of the above-mentioned eigenfunctions.

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