Impurity effects on nano-structured dirty superconductors: violation of Anderson’s Theorem

Abstract

It is shown that in nano-structured s-wave superconductor, transition temperature Tc depends on random impurity potentials. This means violation of the Anderson’s theorem, which states that non-magnetic impurity does not affect the Tc of s-wave superconductor. We determine the impurity effects on Tc for nano-structured superconductor, using the finite element method to solve the Bogoliubov-de Gennes equations under spatially a random impurity potential. We show that some impurity potentials increase Tc but other impurity potentials decrease Tc. We find that the superconductor with localized order parameter shows increased Tc, which is contrary to expectation. Our results show that a dirty superconductor does not always mean weak superconductivity.