Understanding Mott's law from scaling of variable-range-hopping currents and intrinsic current fluctuations

We have used the master equation to simulate variable-range hopping (VRH) of charges in a strongly disordered d-dimensional energy landscape (d=1,2,3). The current distribution over hopping distances and hopping energies gives a clear insight into the difference between hops that occur most frequently, dominate quant. in the integral over the mobility distribution, or are crit. ones that still need to be considered in that integral to recover the full low-temp. mobility. The recently reported scaling with temp. of the VRH-current distribution over hopping distances and hopping energies is quant. analyzed in 1D and 2D, and accurately confirmed. Based on this, we present an anal. scaling theory of VRH, which distinguishes between a scaling part of the distribution and an exponential tail, sepd. by crit. currents that set the scale and that follow self-consistently at each temp. This naturally renders Mott's law for the low-temp. mobility, in a way and with a phys. picture different from that of the established crit.-percolation-network approach to VRH. We argue that current fluctuations as obsd. in simulations are intrinsic to VRH and play an essential role in this distinction. [on SciFinder (R)]