The ac conductivity of the Fermi glass: A model for glassy conduction

Abstract

Analytical expressions for the ac conductivity of the Fermi glass are discussed. At high frequencies an appropriate formulation of the pair approximation in which the conductivity is optimized as a function of the energy range of contributing sites, demonstrates that the loss peak occurs at a frequency, ω c for which the individual pairs form a percolating network. The “percolation” of carriers is associated with the zero frequency limit, as the relaxation times of clusters of impedances are enhanced by factors proportional to the square of their lengths. Critical exponents of percolation theory are relevant in the zero frequency limit, but not above ω c. Above ω c, the small deviation from linearity in the frequency dependence is related to the exact form of the (wide) distribution of individual relaxation times. The theory is in quantitative agreement with experiment in several systems, and describes all general characteristics of the conduction of glasses. Theories which place carrier percolation at ω c, assert either that the critical exponents of percolation theory play no role in the frequency dependence of σ(ω), or that the effects of percolation are felt both above and below the loss peak, and are in error.