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

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.