Pre-Exponential factor and hopping criterion in the Efros-Shklovskii regime*

We address the variable-range hopping regime in the range for which the measured temperature $T$ is of the order of the characteristic Efros-Shklovskii temperature $T_{ES}$. In such a range current theories imply $r_{hop}/\xi<1$, where $r_{hop}$ is the hopping length and $\xi$ is the localization length, clearly in contradiction with the standard criterion for hopping conduction. We consider impurity overlap wavefunctions of the form $\psi(r) \propto r^{-n}\exp(-r/\xi)$ and include the preexponential factor of the resistivity as a logarithmic correction in the Mott optimization procedure. From the general expression derived, the standard Efros-Shklovskii law is recovered for $T<1$, is found for $T_{ES} \geq T$. We argue that the new expression resulting from an interplay between preexponential and exponential factors is a consistent extension of the classical Efros-Shklovskii argument.