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Register a new userA Generic Microscopic Theory for the Universality of TTLS Model Meissner-Berret Ratio in Low-Temperature Glasses
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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 Levelutcite{Joffrin1976}.
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In low-temperature glasses, the sound velocity changes as the logarithmic function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) = mathcal{C}ln(T/T_0)$. With increasing temperature starting from $T=0$K, the sound velocity does not increase monotonically, but reaches a maximum at a few Kelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS) model explained the $ln T$ dependence of sound velocity shift. In TTLS model the slope ratio of $ln T$ dependence of sound velocity shift between lower temperature increasing regime (resonance regime) and higher temperature decreasing regime (relaxation regime) is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-frac{1}{2}$. In this paper we develop the generic coupled block model to prove the slope ratio of sound velocity shift between two regimes is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-1$ rather than $1:-frac{1}{2}$, which agrees with the majority of the measurements. The dielectric constant shift in low-temperature glasses, $[epsilon_r(T)-epsilon_r(T_0)]/epsilon_r(T_0)$, has a similar logarithmic temperature dependence below $10$K: $[epsilon(T)-epsilon(T_0)]/epsilon(T_0) = mathcal{C}ln(T/T_0)$. In TTLS model the slope ratio of dielectric constant shift between resonance and relaxation regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel}=-1:frac{1}{2}$. In this paper we apply the electric dipole-dipole interaction, to prove that the slope ratio between two regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel} = -1:1$ rather than $-1:frac{1}{2}$. Our result agrees with the dielectric constant measurements. By developing a real space renormalization technique for glass non-elastic and dielectric susceptibilities, we show that these universal properties essentially come from the $1/r^3$ long range interactions, independent of the materials microscopic properties.
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