Variable Range Hopping Conduction in Complex Systems and a Percolation Model with Tunneling
| dc.creator | Sen, Asok K. | |
| dc.creator | Bhattacharya, Somnath | |
| dc.date | 2005-06-03 | |
| dc.date.accessioned | 2026-07-07T03:05:28Z | |
| dc.date.available | 2026-07-07T03:05:28Z | |
| dc.description | 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, $G(T) = G_0 {\rm exp}[-(T_0/T)^γ]$, 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 $γ= 1/(d+1)$ 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, $γ=1/2$, {\it independent of d}. Recent experiments indicate that $γ$ 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 $γ$ with $p$, satisfactorily. | |
| dc.description | RevTex4, 4 pages, 5 figures, Presented in conference named "Continuum Models and Discrete Systems" (CMDS10) held in Shoresh, Israel, during 30 June - 04 July, 2003 | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0506089 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0506089 | |
| dc.identifier | "Continuum Models and Discrete Systems," eds. D. Bergman and E. Inan (Kluwer Academic Publishers, Dordrecht, 2004), pp. 367-373 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26462 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Statistical Mechanics | |
| dc.title | Variable Range Hopping Conduction in Complex Systems and a Percolation Model with Tunneling | |
| dc.type | text |