Some remarks on variable range hopping—in particular in the quantum Hall regime

Abstract

An expression for the heat conductivity κ _xx is derived in the effective medium approximation. Mott type formulas are obtained for κ _xx and the Peltier coefficient β _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like$1/\sqrt T$. The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity σ _xx , the results are fully consistent with the experimental data on σ _xx and the density of states at the Fermi level. Finally, β _xx is estimated which together with σ _xx and σ _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients α _xx and ασ _xy .