Coulomb Gap: How a Metal Film Becomes an Insulator

Abstract

Electron tunneling measurements of the density of states (DOS) in ultra-thin Be films reveal that a correlation gap mediates their insulating behavior. In films with sheet resistance $R<5000\Omega$ the correlation singularity appears as the usual perturbative $ln(V)$ zero bias anomaly (ZBA) in the DOS. As R is increased further, however, the ZBA grows and begins to dominate the DOS spectrum. This evolution continues until a non-perturbative $|V|$ Efros-Shklovskii Coulomb gap spectrum finally emerges in the highest R films. Transport measurements of films which display this gap are well described by a universal variable range hopping law $R(T)=(h/2e^2)exp(T_o/T)^{1/2}$.