Statistical Properties of Electric Potentials in a Variable-Range Hopping Regime

Variable-range hopping transport is studied from a new perspective. Unlike the well-known percolation model for variable-range hopping, which treats the connectivity of bonds between a pair of sites, the emphasis here is on the statistical properties of the voltage potential at these sites. The deviations in the voltage potentials are calculated from the rate equations. The variance and power spectra of the deviations show that there are two temperature regimes: nearest-neighbor hopping at high temperatures and variable-range hopping at low temperatures. The development of long-range order between the voltage deviations in the variable-range hopping regime is confirmed by showing the temperature dependence of the correlation length.