Keldysh Ginzburg-Landau action of fluctuating superconductors

Abstract

We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor'kov-Eliashberg coupling between $\Delta$ and the scalar potential, as well as a peculiar nonlocal nonlinear term. The action is gauge invariant and satisfies the fluctuation dissipation theorem. It may be employed e.g. for calculation of higher moments of the current fluctuations.

16 pages, 2 figures

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