VARIABLE RANGE HOPPING CONDUCTION IN COMPLEX SYSTEMS AND A PERCOLATION MODEL WITH TUNNELING

摘要

For the low-temperature electrical conductance of a disordered quantum insulator in d-dimensions, Mott had proposed his Variable Range Hopping (VRH) formula, G(T) = Go 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 found that for a pure (i.e., disorder-free) quantum insulator with interacting charges, γ = 1/2, 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 semi-classical or semi-quantum RRTN (Random Resistor cum Tunneling-bond Network) model, developed by us in the 1990's. These macroscopic granular/percolative composites are built up from randomly placed meso- or nanoscopic coarse-grained clusters, with two pbe-nomenological 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.