Universal crossover in variable range hopping with Coulomb interactions

Using dimensional analysis, we show that the variable-range-hopping resistivity of disordered systems with Coulomb interactions obeys the scaling form ln(/0)=Af(T/Tx), where f(x) is a universal function and A and Tx 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 (fx-1/4) to the Efros-Shklovskii (fx-1/2) behaviors. Data on five different samples of compensated n-type CdSe are shown to collapse onto this single function.