The Thermal Conductivity Plateau in Disordered Systems

The thermal conductivity of disordered substances exhibits a region of weak temperature dependence known as the “plateau” [1]. It occurs in glasses in a temperature range typically between 1 and 20 K. At much lower temperatures, the thermal conductivity is governed by the resonant scattering of thermal phonons from tunneling systems and follows a T2 power law. Above the plateau the temperature dependence is roughly linear in T. Explanations offered for the occurrence of a plateau include: phonon scattering by enhanced densities of tunneling systems [2], elastic scattering by density fluctuations [3], dimensional crossover of the vibrational density of states [4], and weak localization of phonons [5]. As yet there has been no convincing description of this phenomenon.