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

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.

arXiv comment15 pages, 3 figures, to appear in the special JETP issue celebrating E.I. Rashba's 95-th anniversary

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• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Generalized surface multifractality in 2D disordered systems
• Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion
• Boundary multifractality in the spin quantum Hall symmetry class with interaction
• Quantum Fluctuations and Multifractally-Enhanced Superconductivity in Disordered Thin Films
• Superconducting Diode Effect in Weak Localization Regime