Dimensions Effects in Insulating NbTin Disordered Films and Asymptotic Freedom of Cooper Pairs

We investigate the evolution of the electronic transport in disordered NbTiN films at the insulating side of the superconductor-insulator transition as function of the effective system size along the current direction. We demonstrate that both, the threshold voltage characterizing low-temperature superinsulating phase, and the Berezinskii-Kosterlitz-Thouless criticality of the conductance above the superinsulator critical temperature, vanish upon increasing disorder taking the system far from the disorder-driven superconductor-insulator transition. We find that decrease in the system's effective size suppresses its insulating and superinsulating properties and that threshold voltage drops linearly with the diminishing system size. We demonstrate that this linear dependence can be used for experimental measurement of the linear tension of the electric string binding Cooper pairs and anti-Cooper pairs in a superinsulator.