Quantum-critical region of the disorder-driven superconductor-insulator transition

We investigate low temperature transport properties of thin TiN superconducting films, differing by the degree of disorder. At zero magnetic field we find an extremely sharp separation between the superconducting- and insulating phases, indicating a direct superconductor-insulator transition without an intermediate metallic phase. We show that in the critical region of the transition a peculiar highly inhomogeneous insulating state with superconducting correlations forms. The insulating films exhibit thermally activated conductivity and huge positive magnetoresistance at low magnetic fields. A sharp depinning transition at some voltage VT is observed in the I-V curves at very low temperatures. We propose a percolation type of depinning with the threshold voltage determined by the Coulomb blockade energy for the Cooper pairs between neighboring self-induced superconducting islands, with VT being the total voltage along the first conduction path. The observed hysteretic behavior of the threshold and steps on the dI/dV vs. V curves support this percolation picture of the depinning transition.