Superfluid response of two-dimensional filamentary superconductors

Different classes of low-dimensional superconducting systems exhibit an inhomogeneous filamentary superconducting condensate whose macroscopic coherence still needs to be fully investigated and understood. Here, we present a thorough analysis of the superfluid response of a prototypical filamentary superconductor embedded in a two-dimensional metallic matrix. By mapping the system into an exactly solvable random impedance network, we show how the dissipative (reactive) response of the system non-trivially depends on both the macroscopic and microscopic characteristics of the metallic (superconducting) fraction. We compare our calculations with resonant microwave transport measurements performed on LaAlO _3 3 /SrTiO _3 3 heterostructures over an extended range of temperatures and carrier densities finding that the filamentary character of superconductivity accounts for unusual peculiar features of the experimental data.