Temperature dependence of the upper critical field in disordered Hubbard model with attraction

Abstract

We study disorder effects upon the temperature behavior of the upper critical magnetic field in attractive Hubbard model within the generalized $DMFT+\Sigma$ approach. We consider the wide range of attraction potentials $U$ - from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder - from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of $H_{c2}(T)$, especially at low temperatures. In BEC limit and in the region of BCS - BEC crossover $H_{c2}(T)$ dependence becomes practically linear. Disordering also leads to the general growth of $H_{c2}(T)$. In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of transition point and to the increase of $H_{c2}(T)$ in low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of $H_{c2}(T)$ at low temperatures, so that the $H_{c2}(T)$ dependence becomes concave. In BCS - BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to $T_{c}$. However, in the low temperature region $H_{c2}(T)$ may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase $H_{c2}(T=0)$ also making $H_{c2}(T)$ dependence concave.