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Site-disorder driven superconductor-insulator transition: A dynamical mean field study

We investigate the effect of site-disorder on the superconducting (SC) state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength ($U$), the SC order parameter (OP) decreases monotonically with increasing disorder ($x$), while the single-particle spectral gap (SG) decreases for small $x$, reaches a minimum and keeps increasing for larger $x$. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order-parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for $U\rightarrow \infty$. The presence of disorder results in destruction of superconductivity at large $U$, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.