Negative local superfluid densities: The difference between dirty superconductors and dirty Bose liquids

We show that in a distorted superconductor near the superconductor-to-insulator transition, the local superfluid density ${\mathit{N}}_{\mathit{s}}$ fluctuates from point to point in sign as well as magnitude. We demonstrate this explicitly with a simple model in which correlation effects produce a negative Josephson coupling between two superconducting grains. We argue more generally that both correlation effects and resistance fluctuations will produce random signs of ${\mathit{N}}_{\mathit{s}}$. This implies that a disordered superconductor is more like a quantum XY spin glass than a disordered Bose liquid.