Temperature Dependence of Paramagnetic Critical Magnetic Field in Disordered Attractive Hubbard Model

TL;DR

This study investigates how disorder affects the temperature dependence of the paramagnetic critical magnetic field in the attractive Hubbard model across different coupling regimes, revealing universal disorder effects and phase transition behaviors.

Contribution

It introduces a comprehensive analysis of disorder effects on $H_{cp}(T)$ across weak to strong coupling regimes using the DMFT+$ mf extSigma$ approach, highlighting universal disorder influences.

Findings

Growth of coupling strength increases $H_{cp}(T)$ at all temperatures.

Disorder causes a rapid decrease of $H_{cp}(T)$ in weak coupling, but less so in BCS-BEC crossover and BEC limits.

Disorder widens the conduction band, leading to a universal effect on $H_{cp}(T)$ regardless of coupling.

Abstract

Within the generalized DMFT+$\Sigma$ approach we study disorder effects in the temperature dependence of paramagnetic critical magnetic field $H_{cp}(T)$ for Hubbard model with attractive interaction. We consider the wide range of attraction potentials $U$ - from the weak coupling limit, when superconductivity is described by BCS model, up to the limit of very strong coupling, when superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs. The growth of the coupling strength leads to the rapid growth of $H_{cp}(T)$ at all temperatures. However, at low temperatures paramagnetic critical magnetic field $H_{cp}$ grows with $U$ much slower, than the orbital critical field, and in BCS limit the main contribution to the upper critical magnetic filed is of paramagnetic origin. The growth of the coupling strength also leads to the disappearance of the low temperature region of instability towards type I phase transition and Fulde - Ferrell - Larkin - Ovchinnikov (FFLO) phase, characteristic for BCS weak coupling limit. Disordering leads to the rapid drop of $H_{cp}(T)$ in BCS weak coupling limit, while in BCS - BEC crossover region and BEC limit $H_{cp}(T\to 0)$ dependence on disorder is rather weak. Within DMFT+$\Sigma$ approach disorder influence on $H_{cp}(T)$ is of universal nature at any coupling strength and related only to disorder widening of the conduction band. In particular, this leads to the drop of the effective coupling strength with disorder, so that disordering restores the region of type I transition in the intermediate coupling region.