Abstract
We demonstrate that the phonon elastic scattering leads to a dominant dissipation in crystals at low temperature. The two-level systems (TLSs) should be responsible for the elastic scattering, whereas the dissipation induced by static-point defects (SPDs) can not be neglected. One purpose of this work is to show how the energy splitting distribution of the TLS ensemble affects the dissipation. Besides, this article displays the proportion of phonon-TLS elastic scattering to total phonon dissipation. The coupling coefficient of phonon-SPD scattering and the constant P0 of the TLS distribution are important that we estimate their magnitudes in this paper. Our results is useful to understand the phonon dissipation mechanism, and give some clues to improve the performance of mechanical resonators, apply the desired defects, or reveal the atom configuration in lattice structure of disordered crystals.
Highlights
Lower than the energy splittings of most TLSs24
That the point-static defects (PSDs) contribution is taken into account, we estimate the relative contribution from phonon-two-level systems (TLSs) scattering at several temperature after determining the distribution of energy splitting of TLSs
We have introduced the function VP(ε, u) as the distribution density of parameters ε and u, and the total dissipation α is expressed by an integration if these parameters of the TLS ensemble are regarded as a continuous distribution
Summary
Lower than the energy splittings of most TLSs24 This kind of phonon-defect scattering has been proposed before[25], but not derived from a specific perturbation term until recent work in ref. We further discuss the phonon-TLS scattering mechanism under consideration of the PSD scattering mentioned above, and obtain some quantitative results in comparison with the recent experiment[8]. That the PSD contribution is taken into account, we estimate the relative contribution from phonon-TLS scattering at several temperature after determining the distribution of energy splitting of TLSs. In the end, two parameters, including the coupling coefficient K of phonon-SPD scattering and the constant P0 of the TLS distribution, that are crucial for yielding phonon dissipation need to be estimated and discussed. Our results are available for improving and testing the phonon dissipation mechanism, and are helpful to improve the performance of mechanical resonators, apply the desired defects, or reveal the atom configuration in lattice structure of disordered crystals
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