UNIVERSAL CROSSOVER IN VARIABLE RANGE HOPPING WITH COULOMB INTERACTIONS

Using dimensional analysis, we show that the variable-range-hopping resistivity-rho of disordered systems with Coulomb interactions obeys the scaling form ln(rho/rho-0) = Af(T/T(x)), where f(x) is a universal function and A and T(x) are sample-dependent constants. A simple heuristic calculation in three dimensions yields an explicit form for f(x), which exhibits a smooth crossover from the Mott (f is-proportional-to x-1/4) to the Efros-Shklovskii (f is-proportional-to x-1/2) behaviors. Data on five different samples of compensated n-type CdSe are shown to collapse onto this single function.