Universal ratio of TTLS-phonon coupling constants in low-temperature amorphous solids

Abstract

Tunneling-two-level-system model (TTLS model) has successfully explained several universal properties of amorphous solids at low temperatures. The experimentalists found that the ratios of TTLS-phonon coupling constants lie between 1.44 and 1.84 among 16 different amorphous solids, which turns out to be a universal quantity (Berret and Meissner 1988 Z. Phys. B 70 65). However, this universal property remains unexplained. Based on the model introduced by Vural and Leggett (2011 J. Non-Cryst. Solids 357 3528) and real space renormalization, we demonstrate that equals to , where cl and ct are longitudinal and transverse sound velocities, respectively. In this paper, we reveal that this universal quantity essentially comes from the mutual interactions between elementary blocks of amorphous solids, and is insensitive to the microscopic material properties. In the appendix, we also make corrections to the many-body interaction of low-temperature amorphous solids derived by Joffrin and Levelut (1975 J. Physique 36 811).