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Fluctuational Anomalous Hall and Nernst Effects in Superconductors

In this work we develop microscopic kinetic theory of the anomalous Hall and Nernst effects in superconductors induced by fluctuations in the vicinity of the critical transition temperature. The technical analysis is carried out within the Matsubara diagrammatic technique and linear response Kubo formula with disorder averaging and an analytical continuation. It is shown that asymmetric skew-scattering due to spin-orbit interaction gives rise to a new anomalous Hall conductance promoted by Maki-Thompson interference and density of states fluctuational effects. The side-jump mechanism of the anomalous Hall effect is present only in the density of states contributions. The anomalous Nernst effect is found due to a special nonlinear Aslamazov-Larkin term from the quantum-crossing of interacting fluctuations in a Hikami box with the skew-scattering process. In addition to calculations in the weak-coupling BCS model we also sketch an approach for the account of fluctuational transport effects in the strong-coupling limit. In particular we explore an example of how Keldysh version of the Eliashberg theory can in principle be constructed and estimate fluctuation-induced conductivity within conventional electron-phonon coupling scenario. These ideas may pave the way for further developments of strong coupling theories in applications to fluctuations in unconventional superconductors and anomalous transport responses in particular.