Fluctuation Phenomena in Superconductors

Reading a major part of the textbooks one can have impression that the BCS theory of superconductivity is the exact one. Proposed review dispels this delusion, clearly indicating the limits of the mean field theory applicability and demonstrating existence of the wide circle of interesting phenomena being beyond its confines. The chapter presents itself both the review and the textbook of fluctuation phenomena in superconductors. Its first half is devoted to presentation of the phenomenological and microscopical methods in the description of fluctuations. The Ginzburg-Landau functional and corresponding general description of fluctuation thermodynamics in framework of the functional integration over fluctuation fields approach is introduced. Time-dependent Ginzburg-Landau equation is is applied for the description of the fluctuation transport in the vicinity of superconducting transition. The basic aspects of the microscopic description of fluctuation phenomena in superconductors in the frameworks of the quantum field theory are presented. In the second half the authors portray a panorama of the superconductive fluctuations manifestation in different observables. The microscopic analysis of the different fluctuation contributions to the conductivity, magnetoconductivity, Hall effect, tunneling conductivity, thermopower, NMR relaxation rate is presented. The physical origin of Aslamazov-Larkin, Maki-Thompson and density of states renormalization corrections are discussed.