Superconductor-insulator transition in ultrathin Pb films: Localization and superconducting coherence

We have measured temperature-dependent resistivities of a set of Pb ultrathin films by repeating in situ deposition at liquid-He temperature. Observed conductance in the fermion region can be described by a single-parameter scaling function ($\beta$ function) with a self-consistent theory for localization in two dimensions. Based on estimated values of electrical localization length (${\xi }_{\mathrm{loc}}$) and superconducting coherence length (${\xi }_{\mathrm{super}}$), the superconductor-insulator transition is confirmed to occur at the point where ${\xi }_{\mathrm{loc}}\sim 2{\xi }_{\mathrm{super}}$. Moreover, only samples exhibiting $\ln T$ dependence in the fermion region become global coherent superconductors at low temperature.