Consistent hopping criterion in the Efros-Shklovskii regime

We address the variable-range hopping regime in the domain where the measuring temperature T is of the order of the characteristic Efros-Shklovskii temperature TES. In such a range, current theories imply rhop ξ<1, where rhop is the hopping length and ξ is the localization length, clearly in contradiction with the standard criterion for hopping conduction. We consider impurity overlap wave functions of the form ψ (r) r-n exp (-r ξ) and include the preexponential factor of the hopping probability as a logarithmic correction in the Mott optimization procedure. From the general expressions derived, the standard Efros-Shklovskii law is recovered for T TES, whereas an extended preexponential sensitive regime, consistent with rhop ξ>1, is found for TES T. We argue that the expression resulting from an interplay between preexponential and exponential factors is a consistent extension of the classical Efros-Shklovskii argument. An additional parameter in the theory is directly related to the decay of the impurity wave functions and could be seen as a probe into their behavior. A fit of reference experimental data to the proposed theory yields consistent results.