Multifractally-Enhanced Superconductivity in Two-Dimensional Systems with Spin-Orbit Coupling

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.

Automated summary

This study investigates the multifractally enhanced superconducting states in two-dimensional systems with the interplay of Anderson localization and electron-electron interactions in the presence of spin-orbit coupling. The energy dependence of the superconducting spectral gap is found to be induced by multifractal correlations. The superconducting transition temperature and spectral gap are determined for different coupling cases. Mesoscopic fluctuations of the local density of states in the superconducting state are also studied, and it is found that spin-orbit coupling reduces the amplitude of fluctuations.