Aharonov-Bohm oscillations with periodhc/4eand negative magnetoresistance in dirty superconductors

We show that in a disordered 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 correlation effects and resistance fluctuations produce random signs of ${\mathit{N}}_{\mathit{s}}$. This implies that the superconductor-to-insulator transition may not be in the same universality class as the Bose-superfluid–to–insulator transition. It also results in a hc/4e period of Aharonov-Bohm oscillations and a negative magnetoresistance; both occur for T>${\mathit{T}}_{\mathit{c}}$ in superconducting samples and at low temperatures in insulating samples.