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.Comment: 15 pages, 3 figures, to appear in the special JETP issue celebrating E.I. Rashba's 95-th anniversar

Chirality inversion and radius blow-up of a N\'eel-type skyrmion by a Pearl vortex

We develop a theory for the coaxial configuration of a N\'eel-type skyrmion and a Pearl vortex in thin superconductor-chiral ferromagnetic heterostructures. Using direct numerical solution of the Euler-Lagrange equation and micromagnetic simulations we demonstrate that the inhomogeneous magnetic field of the Pearl vortex significantly modifies the skyrmion profile with respect to the one in the absence of the vortex. We discover drastic enlargement of the skyrmion's radius and inversion of the skyrmion's chirality. To unravel physics behind these effects we invent novel two-parameter ansatz for the magnetization profile of the skyrmion in the presence of the vortex. Chirality inversion and radius blow-up are controlled not only by the material parameters of the heterostructure but also by the thickness of the superconductor. Our findings can have implications for Majorana modes localized at skyrmion-vortex pairs.Comment: 6 pages, 2 figures; 1 video file and its description (as ancillary files