Ginzburg-Landau expansion and the upper critical field in the disordered attractive Hubbard model (brief review)

We present a brief review of our studies of disorder influence upon Ginzburg-Landau expansion coefficients in Anderson-Hubbard model with attraction in the framework of the generalized DMFT + $\Sigma$ approximation. A wide range of attractive potentials $U$ is considered from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to the Bose-Einstein condensation of compact Cooper pairs, which are formed at temperatures significantly higher than the superconducting transition temperature, as well as the wide range of disorders from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field $H_{c2}(T)$, which demonstrates the anomalies due both to the growth of attractive potential and to the effects of strong disordering.