Universal time-temperature scaling of conductivities in random site energy and associated random barrier model

Universal time-temperature scaling of conductivity spectra in disordered solids has been explained by thermally activated hopping of noninteracting particles over random energy barriers. An open problem is whether the random barrier model accounts for site energy disorder in real materials. Through mapping many-particle hopping in a disordered site energy landscape to that of independent particles in a barrier landscape, we show that time-temperature scaling is correctly described by the associated barrier model in the low temperature limit. However, the site energy model displays good scaling behavior at substantially higher temperatures than the barrier model, in agreement with experimental observations. Extending the mapping to different types of mobile charge carriers allows us to understand why time-temperature superposition can be absent in mixed alkali glasses.