Dielectric Response of a Superionic Conductor

A microscopic theory of ionic transport in superionic conductors is presented. Based on a liquidlike description of the ionic carriers, it describes the frequency and temperature dependences of the conductivity. A sum rule is obtained and the theory predicts the existence of a conductivity peak which scales with the inverse of the ionic carrier mass. The results are in good agreement with recent data on Na and Ag $\beta$-aluminas.