The Density of Tunneling and Vibrational States of Glasses within the Soft-Potential Model

Abstract

Numerical calculations of the density of tunneling and vibrational states of glasses within the soft‐potential model (an extension of the tunneling model to include soft vibrations) are reported and compared to analytical approximations. Using a specific assumption on the asymmetry of the soft potentials, one is able to describe the anomalous features of the specific heat Cp and the thermal conductivity of glasses over the entire low temperature range, up to and including the peak in Cp/T3 and the second rise of the thermal conductivity above the plateau.

Evidence of universality in the dynamical response of micromechanical diamond resonators at millikelvin temperatures

“…The Soft potential Model (SPM) assumes a quartic potential and constant density of states for each mode, based on the concept of localized low frequency sound waves. The SPM is successful in explaining low temperature thermal conductivity and predicts a Q −1 ∝ T 3 4 dissipation law with low temperature saturation [13]. Standard single crystal models predict non-logarithmic temperature dependence of the frequency shift and non-power-law temperature dependence of the dissipation, in contrast to the data presented here.…”

“…Even though the general trend of the low temperature dependence is easily explained by the standard glass model of TLS [9,10], additional experiments in other materials such as silicon [8] and gallium arsenide [11] and detailed theoretical calculations [12,13] suggest an incomplete understanding of the temperature dependence of the quality factor.…”

Heat capacity and thermodynamic functions of zirconia and yttria-stabilized zirconia

“…The excess low-frequency vibrational modes in glasses is assumed to be attributed to strong scattering of sound waves by disorders in the material, (27) a topologically disordered structure, and a distribution of force constant, or to a soft local vibrational mode. (28) The defects in yttria-stabilized zirconia crystal such as oxygen vacancies, substituting yttrium ions, and lattice strain may correspond to these mechanisms. Further investigation on the relationship between the low-energy modes and defect structure of yttria-stabilized zirconia may throw light on the low-temperature properties of disordered materials.…”

Quasi‐localized low‐frequency vibrational modes of disordered solids I. Study by photon echo

“…According to Ref. [31], E b can be consider as an upper limit of the soft modes energy (see Fig. 2a).…”