ANOMALOUS FREQUENCY-DEPENDENT CONDUCTIVITY IN DISORDERED ONE-DIMENSIONAL SYSTEMS

Conduction by classical charge carriers is investigated for a one-dimensional system interrupted by barriers with a random distribution of activation energies. Under certain conditions the transport properties are dominated by disorder, and the model predicts an anomalous low-frequency conductivity σ(ω)∼(-iω)ν, with ν=(1-TTm)(1+TTm), for T<Tm, and a mobility transition at T=Tm. The model is shown to describe recent experiments on the one-dimensional superionic conductor hollandite (K1.54Mg0.77Ti7.23O16). © 1979 The American Physical Society.