Coulomb Gap: How a Metal Film Becomes an Insulator

Electron tunneling measurements of the density of states (DOS) in ultrathin Be films reveal that a correlation gap mediates their insulating behavior. In films with sheet resistance R<5000 Ω 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 nonperturbative \|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\(T\) = \(h/2e²\)exp\(T₀/T\)^1/2.