Generalization of Anderson's theorem for disordered superconductors

John F. Dodaro; Steven A. Kivelson

doi:10.1103/PhysRevB.98.174503

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Generalization of Anderson's theorem for disordered superconductors

John F. Dodaro, Steven A. Kivelson

DOI 10.1103/PhysRevB.98.174503 · Physical Review B

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Abstract

We show that at the level of BCS mean-field theory, the superconducting Tc is always increased in the presence of disorder, regardless of order parameter symmetry, disorder strength, and spatial dimension. This result reflects the physics of rare events—formally analogous to the problem of Lifshitz tails in disordered semiconductors—and arises from considerations of spatially inhomogeneous solutions of the gap equation. So long as the clean-limit superconducting coherence length, ξ0, is large compared to disorder correlation length, a, when fluctuations about mean-field theory are considered, the effects of such rare events are small (typically exponentially in [ξ0/a]d); however, when this ratio is ∼1, these considerations are important. The linearized gap equation is solved numerically for various disorder ensembles to illustrate this general principle.