Disorder Effects in BCS-BEC Crossover Region of Attractive Hubbard Model

TL;DR

This paper investigates how disorder influences the superconducting transition temperature and local pair formation across the BCS-BEC crossover in the attractive Hubbard model, revealing disorder can both suppress and enhance T_c depending on interaction strength.

Contribution

It demonstrates that disorder effects on T_c and local pairs are primarily due to band-widening, extending the Anderson theorem across the crossover.

Findings

Disorder suppresses T_c in weak coupling regime.

Disorder enhances T_c in strong coupling regime.

Changes in T_c are linked to effective bandwidth modifications.

Abstract

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.