Measuring the Localization Length through the superconductor-insulator transition in ultrathin amorphous beryllium films

Electron transport and tunneling across the superconductor-insulator (SI) transition have been measured simultaneously for quench-condensed ultrathin amorphous beryllium films. The anomalous negative magnetoresistance previously observed in insulating films disappears when Mn impurities are introduced to the films, restoring a rather clean Efros-Shklovskii type hopping behavior. The combination of transport and tunneling data allows us to determine, independently and up to a constant on the order of unity, the localization length, \xi_{L}, and the dielectric constant, \kappa, for the films. As the normal-state sheet resistance of the films at 20 K is reduced with increasing film thickness, \xi_{L} increases exponentially. The SI transition occurs when \xi_{L} crosses the Ginzburg-Landau coherence length, \xi_{S}.