Gap States in Dilute Magnetic Alloy Superconductors

We study states in the superconducting gap induced by magnetic impurities using self-consistent quantum Monte Carlo with maximum entropy and formally exact analytic continuation methods. The magnetic impurity susceptibility has different characteristics for $T_0\lesssim T_{c0\mathrm{}}$ and $T_0\gtrsim T_{c0\mathrm{}}$ ( $T_0$: Kondo temperature; $T_{c0\mathrm{}}$: superconducting transition temperature) due to the crossover between a doublet and a singlet ground state. We systematically study the location and the weight of the gap states and the gap parameter as a function of $T_0/T_{c0\mathrm{}}$ and the concentration of the impurities.