A microscopic treatment of the consequences for superconductivity of a nonconstant electronic density of states is presented. Generalized Eliashberg gap equations valid for a varying density of states are presented, from which the change of $T_c$ with static or thermal disorder can be calculated. The temperature dependence of the effective mass is shown to be altered by disorder. Use of these results provides a possible experimental approach for deducing the energy variation of the density of states of superconductors.

• Received 16 July 1979

DOI:https://doi.org/10.1103/PhysRevB.21.3897