Measurement of the Localization Length through the superconductor-insulator transition of ultrathin amorphous beryllium films

Based on the Efros-Shklovskii behavior observed in electron transport and tunneling, we have determined, independently and up to a constant on the order of unity, the localization length and the dielectric constant for quench-condensed ultrathin amorphous beryllium films. As the normal-state sheet resistance of the films at 20 K is reduced with increasing film thickness, the localization length increases exponentially. The superconductor-insulator transition occurs when the localization length crosses the Ginzburg-Landau coherence length. We discuss the implication of these results on a number of issues regarding superconductivity in the strongly disordered regime.