Disorder effects in BCS–BEC crossover region of attractive Hubbard model

We study the disorder effects upon superconducting transition temperature $T_c$ and the number of local pairs in attractive Hubbard model within the combined Nozieres–Schmitt-Rink and DMFT+$\Sigma$ approximations. We analyze the wide range of attractive interaction $U$, from the weak coupling region, where instability of the normal phase and superconductivity are well described by BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose–Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress $T_c$ in the weak coupling limit, or significantly enhance $T_c$ in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes of $T_c$ are related to change of the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-widening effects.