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

TL;DR

This study investigates the normal phase of the attractive Hubbard model across various interaction strengths using DMFT with NRG, revealing how disorder affects superconducting instability and confirming the robustness of the Anderson theorem.

Contribution

It provides a comprehensive analysis of the normal phase properties and superconducting transition dependence on interaction strength and disorder within the attractive Hubbard model.

Findings

Disorder has a weak effect on the critical temperature $T_c$.

Superconducting instability varies smoothly from BCS to Bose-condensation regimes.

Normal phase spectral properties are characterized across interaction strengths.

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.