Proposal for a pre-exponential dependent Efros-Shklovskii regime

We address the variable range hopping regime in the range for which the measured temperatures are of the order of the characteristic Mott or Efros-Shklovskii temperatures $T_M$ and $T_{ES}$ respectively. In such a range present theories imply $R_{hop}/\xi<1$ where $R_{hop}$ is the hopping length and $\xi$ is the localization length. Using the Mott optimization procedure, including prefactor corrections in the wavefunction overlap, we obtain expressions for the dependence on temperature for the typical hopping length and the resistivity in an Anderson insulator with coulombic interactions. Such expressions lead to a regular Efros-Shklovskii law when $T<1$. We propose that the optimization procedure can consistently explain contradictory results in the critical regime and recent experimental results showing a maximum in resistivity due to a interplay between prefactor and exponential terms.