We have investigated the effect of the long-range Coulomb interaction on the one-particle excitation spectrum of $n$-type germanium, using tunneling spectroscopy on mechanically controllable break junctions. At low temperatures, the tunnel conductance shows a minimum at zero bias voltage due to the Coulomb gap. Above 1 K, the gap is filled by thermal excitations. This behavior is reflected in the variable-range hopping resistivity measured on the same samples: up to a few degrees Kelvin the Efros-Shklovskii $\ln R\propto T^{-1\mathrm{}/2}$ law is obeyed, whereas at higher temperatures deviations from this law occur. The type of crossover differs from that considered previously in the literature.

• Received 26 June 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1845