Ginzburg-Landau expansion and the upper critical field in disordered attractive Hubbard model

TL;DR

This paper reviews how disorder affects the Ginzburg-Landau coefficients and upper critical field in the attractive Hubbard model across weak to strong coupling regimes, including near Anderson transition.

Contribution

It provides a comprehensive analysis of disorder effects on superconductivity parameters in the attractive Hubbard model using the DMFT+Σ approximation, covering a wide range of coupling and disorder strengths.

Findings

Disorder influences Ginzburg-Landau coefficients significantly.

Upper critical field exhibits anomalies with increasing attraction and disorder.

Superconducting transition varies from BCS to BEC regimes.

Abstract

We present a short review of our studies of disorder influence upon Ginzburg - Landau expansion coefficients in Anderson - Hubbard model with attraction in the framework of the generalized DMFT+$\Sigma$ approximation. A wide range of attractive potentials $U$ is considered - from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs, which are formed at temperatures significantly higher than the temperature of superconducting transition, as well as the wide range of disorders - from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field $H_{c2}(T)$, which demonstrates the anomalies both due to the growth of attractive potential and the effects of strong disordering.