Superfluid Weight of Strongly Inhomogeneous Superconductors

Abstract

In this work, we obtain the expression, within the linear response approximation, that allows the direct calculation of the superfluid weight for strongly inhomogeneous superconductors. Using this expression, we find that, in general, the correction to the superfluid weight due to the response of the superconductor's pairing potential to the perturbing vector potential is important in superconductors with a strongly inhomogeneous pairing potential. We consider two exemplary cases: the case when strong inhomogeneities in the pairing potential are induced by a periodic potential, and the case when superconducting vortices are induced by an external magnetic field. For both cases we show that the correction to the superfluid weight due to the response of the paring potential to the perturbing vector potential can be significant, it must be included to obtain quantitatively correct results, and that for the case when vortices are present the expression of the superfluid weight that does not include such correction returns qualitatively wrong results.