Localized superconductivity in the quantum-critical region of the disorder-driven superconductor-insulator transition in TiN thin films

We investigate low-temperature transport properties of thin TiN superconducting films in the vicinity of the disorder-driven superconductor-insulator transition. In a zero magnetic field, we find an extremely sharp separation between superconducting and insulating phases, evidencing a direct superconductor-insulator transition without an intermediate metallic phase. At moderate temperatures, in the insulating films we reveal thermally activated conductivity with the magnetic field-dependent activation energy. At very low temperatures, we observe a zero-conductivity state, which is destroyed at some depinning threshold voltage V-T. These findings indicate the formation of a distinct collective state of the localized Cooper pairs in the critical region at both sides of the transition.