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Validity of Anderson's theorem for s-wave superconductors

We investigate validity of Anderson's theorem (AT) for disordered s-wave superconductors in a negative U Hubbard model with random on-site energies, $ε_{i}$. The superconducting critical temperature, $T_{c}$, is calculated in the coherent potential approximation (CPA) as a function of impurity concentration, $c$, the random potentials for different band filling. In contradiction to Anderson's theorem, we found that $T_{c}$ is dramatically sensitive with respect to $c$ and $ε_{i}$. Our results shows that for low impurity concentrations and weak on-site energies, $ε_{i}$, the AT is valid, while in the strong scattering limit even for low impurity concentration, $T_{c}$ is very small with respect to the clean system and by increasing $c$ it is completely suppressed, hence AT is violated in this regime.