Attractive Hubbard Within the Generalized DMFT: Normal State Properties, Disorder Effects and Superconductivity

Using the generalized DMFT+ Σ approach, we have studied disorder influence on the density of states, optical conductivity of the normal phase, superconducting transition temperature, and Ginzburg–Landau coefficients in the attractive Hubbard model. The wide range of attractive potentials U was studied—from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong coupling region, where superconducting transition is due to the Bose–Einstein condensation (BEC) of preformed Cooper pairs. For semi-elliptic “bare” density of states of conduction band, the disorder influence on all single-particle properties (e.g., density of states) is universal for arbitrary strength of electronic correlations and is due only to the general disorder widening of conduction band. Using the combination of DMFT +Σ and Nozieres–Schmitt-Rink approximations, we have studied the disorder influence upon superconducting transition temperature Tc for the range of characteristic values of U and disorder including the BCS-BEC crossover region. Disorder can either suppress Tc (in the weak coupling region) or significantly increase Tc (in strong coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of superconducting critical temperature are essentially due only to the general disorder widening of the conduction band.