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Interplay of Superconductivity and Spin-Dependent Disorder

The finite temperature phase diagram for the 2D attractive fermion Hubbard model with spin-dependent disorder is considered within Bogoliubov-de Gennes mean field theory. Three types of disorder are studied. In the first, only one species is coupled to a random site energy; in the second, the two species both move in random site energy landscapes which are of the same amplitude, but different realizations; and finally, in the third, the disorder is in the hopping rather than the site energy. For all three cases we find that, unlike the case of spin-symmetric randomness, where the energy gap and average order parameter do not vanish as the disorder strength increases, a critical disorder strength exists separating distinct phases. In fact, the energy gap and the average order parameter vanish at distinct transitions, $V_{c}^{\rm gap}$ and $V_{c}^{\rm op}$, allowing for a gapless superconducting (gSC) phase. The gSC phase becomes smaller with increasing temperature, until it vanishes at a temperature $T^{\ast}$.