A unified equivalent-circuit approach to the theory of AC and DC hopping conductivity in disordered systems

The Miller-Abrahams equivalent circuit is used to motivate an extension of the pair approximation to the AC hopping conductivity sigma ( omega ) of a random system, which embraces the DC limit sigma (0). The theory is simple to develop and readily yields both analytical and numerical results. The formulae obtained reproduce the pair approximation in the low-density limit and give known exact asymptotic results at high densities and high frequencies. The numerical predictions of the theory are compared with data obtained by direct numerical solution of Kirchhoff's equations for random networks. Excellent agreement is obtained for sigma (0) for energy-independent and energy-dependent hopping in 2D and 3D, and for sigma ( omega ) for energy-independent hopping in 3D.