Frequency dependence of ionic conductivity in a two-dimensional system of Ag β-alumina

Measurements of the complex impedance of a single crystal of Ag β-alumina have been made in the frequency range of 1 Hz–106 Hz. Ag β-alumina is an ideal two-dimensional superionic conductor (SIC). The slope of AC conductivity σ(ω) was investigated in the temperature range from approximately 100 K to room temperature. A small power-law dependence σ(ω) ∝ ωs was found, with the slope s being evaluated as 0.11–0.15. In the present study, a “scale-invariance” for SIC with a two-dimensional disordered system was suggested from the small power-law dependence.