Random local attraction driven metal-superconductor transitions

In this paper, we investigate the disordered attractive Hubbard model by combining dynamical mean field theory, coherent potential approximation and iterated perturbation theory for superconductivity as an impurity solver. Disorder is introduced in the local attraction $U$. We assume that $U$ is distributed according to a bimodal probability distribution, wherein an $x$ fraction of sites are pairing centers ($U\neq0$) and $(1-x)$ fraction of sites are non-interacting ($U=0$). It is found that beyond a critical $x=x_c$, a first order metal-superconductor phase transition leads to superconductivity being induced in the interacting as well as non-interacting.