A Generic Microscopic Theory for the Universality of TTLS Model Meissner-Berret Ratio in Low-Temperature Glasses

Abstract

Tunneling-two-level-system (TTLS) model has successfully explained several low-temperature glass universal properties which do not exist in their crystalline counterparts. The coupling constants between longitudinal and transverse phonon strain fields and two-level-systems are denoted as $\gamma_l$ and $\gamma_t$. The ratio $\gamma_l/\gamma_t$ was observed to lie between $1.44$ and $1.84$ for 18 different kinds of glasses. Such universal property cannot be explained within TTLS model. In this paper by developing a microscopic generic coupled block model, we show that the ratio $\gamma_l/\gamma_t$ is proportinal to the ratio of sound velocity $c_l/c_t$. We prove that the universality of $\gamma_l/\gamma_t$ essentially comes from the mutual interaction between different glass blocks, independent of the microscopic structure and chemical compound of the amorphous materials. In the appendix we also give a detailed correction on the coefficient of non-elastic stress-stress interaction $\Lambda_{ijkl}^{(ss')}$ which was obtained by Joffrin and Levelut\cite{Joffrin1976}.