Scaling of current distributions in variable-range hopping transport on two- and three-dimensional lattices

From extensive computer simulations of variable-range hopping (VRH) transport of charges on regular two- and three-dimensional lattices with random site energies we calculate the average contribution to the total current of hops over a certain distance and with a certain hop energy. We find that the resulting current distribution is a universal function of scaled distance and energy variables. We discuss this scaling in the light of the original arguments of Mott and percolation arguments to explain the temperature dependence of the VRH conductivity