Localized Superconductivity in the Quantum-Critical Region around the Disorder-Driven Superconductor-Insulator Transition

We investigate low-temperature transport properties of thin TiN superconducting films, which differ in the degree of disorder. In zero magnetic field, we find an extremely sharp separation between superconducting- and insulating phases, demonstrating a direct superconductor-insulator transition without an intermediate metallic phase. Temperature- and magnetic field behaviors of the resistance reveal an insulating trend in the superconducting films and a superconducting trend in insulating films. The conductivity of the insulating films is thermally activated. A sharp depinning threshold voltage V_T is observed in the I-V curves at very low temperatures. These observations suggest a distinct collective state with localized Cooper pairs to form in the critical region of the transition