Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

Abstract

We study the normal (non-superconducting) phase of attractive Hubbard model within dynamical mean field theory (DMFT) using numerical renormalization group (NRG) as impurity solver. Wide range of attractive potentials $U$ is considered, from the weak-coupling limit, where superconducting instability is well described by BCS approximation, up to the strong-coupling region, where superconducting transition is described by Bose-condensation of compact Cooper pairs, which are formed at temperatures much exceeding superconducting transition temperature. We calculate density of states, spectral density and optical conductivity in the normal phase for this wide range of $U$, including the disorder effects. Also we present the results on superconducting instability of the normal state dependence on the attraction strength $U$ and the degree of disorder. Disorder influence on the critical temperature $T_c$ is rather weak, suggesting in fact the validity of Anderson theorem, with the account of the general widening of the conduction band due to disorder.