T_c of disordered superconductors near the Anderson transition

TL;DR

This paper investigates whether the critical temperature of disordered superconductors deviates from the Anderson theorem near the localization transition, finding that strong local effects can cause deviations, but not due to fractal superconductivity.

Contribution

The study systematically examines violations of the Anderson theorem near the localization transition, highlighting the role of impurity resonances and local effects over fractal superconductivity.

Findings

Deviations from the Anderson theorem are possible due to impurity resonances.

Localization of the order parameter can occur at atomic scales.

No evidence supports fractal superconductivity near the transition.

Abstract

According to the Anderson theorem, the critical temperature T_c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a self-averaging order parameter, which can be violated in the strong localization region. Stimulating by statements on the essential increase of T_c near the Anderson transition, we carried out the systematic investigation of possible violations of self-averaging. Strong deviations from the Anderson theorem are possible due to resonances at the quasi-discrete levels, resulting in localization of the order parameter at the atomic scale. This effect is determined by the properties of individual impurities and has no direct relation to the Anderson transition. In particular, we see no reasons to say on "fractal superconductivity" near the localization threshold.