Variable Range Hopping Conduction in Complex Systems and a Percolation Model with Tunneling

Details Variable Range Hopping Conduction in Complex Systems and a Percolation Model with Tunneling Variable Range Hopping Conduction in Complex Systems and a Percolation Model with Tunneling

2005-06-03

arxiv.org/abs/cond-mat/0506089v1

"Continuum Models and Discrete Systems," eds. D. Bergman and E. Inan (Kluwer Academic Publishers, Dordrecht, 2004), pp. 367-37

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTex4, 4 pages, 5 figures, Presented in conference named "Continuum Models and Discrete Systems" (CMDS10) held in Shoresh, I

Scientific paper

For the low-temperature electrical conductance of a disordered {\it quantum insulator} in $d$-dimensions, Mott \cite{mott} had proposed his Variable Range Hopping (VRH) formula, $G(T) = G_0 {\rm exp}[-(T_0/T)^{\gamma}]$, where $G_0$ is a material constant and $T_0$ is a characteristic temperature scale. For disordered but non-interacting carrier charges, Mott had found that $\gamma = 1/(d+1)$ in $d$-dimensions. Later on, Efros and Shkolvskii \cite{esh} found that for a pure ({\it i.e.}, disorder-free) {\it quantum insulator} with interacting charges, $\gamma =1/2$, {\it independent of d}. Recent experiments indicate that $\gamma$ is either (i) larger than any of the above predictions; and, (ii) more intriguingly, it seems to be a function of $p$, the dopant concentration. We investigate this issue with a {\it semi-classical} or {\it semi-quantum} RRTN ({\it Random Resistor cum Tunneling-bond Network}) model, developed by us in the 1990's. These macroscopic {\it granular/ percolative composites} are built up from randomly placed meso- or nanoscopic coarse-grained clusters, with two phenomenological functions for the temperature-dependence of the metallic and the semi-conducting bonds. We find that our RRTN model (in 2D, for simplicity) also captures this continuous change of $\gamma$ with $p$, satisfactorily.

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