Superfluid Stiffness in Inhomogeneous and Disordered Superconductors

The superfluid stiffness is a key property of superconductors, but in inhomogeneous systems, conventional linear response calculations miss crucial corrections from the pairing potential's response to an external vector potential. We introduce a general framework incorporating these effects for accurate results. We examine examples including periodic potential-induced inhomogeneities and magnetic-field vortices, where corrections lead to notable quantitative and qualitative differences. We further apply this to disordered superconductors with non-magnetic and magnetic impurities, studying trivial and topological systems. Relevance to moiré multilayers and vortex pinning for enhanced critical currents is discussed.