Attractive Hubbard model with disorder and the generalized Anderson theorem

TL;DR

This paper investigates how disorder affects single-particle properties and superconducting transition temperature in the attractive Hubbard model across different coupling regimes, confirming the generalized Anderson theorem's validity.

Contribution

It applies the DMFT+Sigma approach to study disorder effects in the attractive Hubbard model, covering BCS to BEC regimes and different density of states models, revealing universal behavior and disorder influence on T_c.

Findings

Disorder universally widens the conduction band in semi-elliptic density of states.

In flat density of states, disorder effects are mainly due to band widening, with universality restored at high disorder.

Disorder can suppress or enhance T_c depending on the coupling strength, consistent with the generalized Anderson theorem.

Abstract

Using the generalized DMFT+Sigma approach we have studied disorder influence on single-particle properties of the normal phase and superconducting transition temperature in 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 BCS model, towards the strong coupling region, where superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the temperature of superconducting transition. We have studied two typical models of conduction band with semi-elliptic and flat densities of states, appropriate for three-dimensional and two-dimensional systems respectively. For semi-elliptic density of states disorder influence on all single-particle properties (e.g. density of states) is universal for arbitrary strength of electronic correlations and disorder and is due only to the general disorder widening of conduction band. In the case of flat density of states universality is absent in general case, but still the disorder influence is due mainly to band widening and universal behavior is restored for large enough disorder. Using the combination of DMFT+Sigma and Nozieres - Schmitt-Rink approximations we have studied disorder influence upon superconducting transition temperature T_c for the range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong coupling. Disorder can either suppress T_c (in the weak coupling region) or significantly increase T_c (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.