2005/06/03 by Asok K. Sen, Somnath Bhattacharya
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech
published as "Continuum Models and Discrete Systems," eds. D. Bergman and E. Inan (Kluwer Academic Publishers, Dordrecht, 2004), pp. 367-373 · 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
arxiv created 2005/06/03 · arxiv updated 2009/12/01
For the low-temperature electrical conductance of a disordered \it quantum insulator in d-dimensions, Mott \citemott had proposed his Variable Range Hopping (VRH) formula, G(T) = G0 \rm exp[-(T0/T)γ], where G0 is a material constant and T0 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 \citeesh 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.