Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling

TL;DR

This paper develops a theory for how multifractality enhances superconductivity in two-dimensional systems with spin-orbit coupling, showing increased transition temperatures and spectral gaps due to disorder and interactions.

Contribution

It introduces a modified theoretical framework incorporating spin-orbit coupling into multifractally-enhanced superconductivity in 2D systems, deriving new equations for spectral gaps and transition temperatures.

Findings

Multifractality increases superconducting transition temperature.

Spectral gap becomes energy-dependent with spin-orbit coupling.

Spin-orbit coupling reduces mesoscopic fluctuations of the local density of states.

Abstract

The interplay of Anderson localization and electron-electron interactions is known to lead to enhancement of superconductivity due to multifractality of electron wave functions. We develop the theory of multifractally-enhanced superconducting states in two-dimensional systems in the presence of spin-orbit coupling. Using the Finkel'stein nonlinear sigma model, we derive the modified Usadel and gap equations that take into account renormalizations caused by the interplay of disorder and interactions. Multifractal correlations induce energy dependence of the superconducting spectral gap. We determine the superconducting transition temperature and the superconducting spectral gap in the case of Ising and strong spin orbit couplings. In the latter case the energy dependence of superconducting spectral gap is convex whereas in the former case (as well as in the absence of spin-orbit coupling) it is concave. Multifractality enhances not only the transition temperature but, in the same way, the spectral gap at zero temperature. Also we study mesoscopic fluctuations of the local density of states in the superconducting state. Similarly to the case of normal metal, spin-orbit coupling reduce the amplitude of fluctuations.