Ginzburg - Landau Expansion in BCS - BEC Crossover Region of Disordered Attractive Hubbard Model

TL;DR

This paper investigates how disorder affects the Ginzburg-Landau coefficients and superconducting properties across the BCS-BEC crossover in the attractive Hubbard model, revealing universal behaviors and disorder insensitivity in certain parameters.

Contribution

It provides a detailed analysis of disorder effects on Ginzburg-Landau coefficients in the BCS-BEC crossover, highlighting universal behaviors and the varying impact of disorder across different coupling regimes.

Findings

Disorder universally influences coefficients A and B, related to the density of states.

Superconducting critical temperature T_c exhibits universal behavior under disorder.

Coefficient C is suppressed by disorder in weak coupling but nearly independent in strong coupling.

Abstract

We have studied disorder effects on the coefficients of Ginzburg - Landau (GL) expansion for attractive Hubbard model within the generalized DMFT+Sigma approximation for the wide region of the values of attractive potential U - from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature T_c (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of "dirty" superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS - BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at T_c, in BCS - BEC crossover and strong coupling regions.