Cluster approximation in the theory of the AC hopping conductivity in disordered systems. II. The three-dimensional case

For pt.I see ibid., vol.12, p.2797 (1979). AC hopping conductivity calculations are performed using a method analogous to the one used in percolation theory for frequencies lower than those described by two-site models. An expression was obtained for sigma ( omega ) approximately omega f( omega tau c ), f being a slowly decreasing function of omega tau c ( tau c is a few orders of magnitude larger than the characteristic time in two-site models, tau 0 approximately 1/ nu ph ). Over a wide frequency range sigma ( omega ) approximately omega s , with s<1, and s may depend on omega , temperature and concentration of localisation centres. Agreement between the theory and the available experimental data is discussed.