Scattering of phonons on two-level systems in disordered crystals

TL;DR

This paper investigates how phonons scatter off two-level systems in disordered crystals, highlighting the anisotropic interactions and broader variability in scattering ratios compared to isotropic solids.

Contribution

It introduces a model linking two-level systems to strain fields via a tensor aligned with elastic constants, emphasizing anisotropic phonon interactions in disordered crystals.

Findings

Scattering rates depend on crystal symmetry and disorder.

The ratio of longitudinal to transverse coupling constants varies widely.

Anisotropic interactions are more pronounced in disordered crystals.

Abstract

We calculate the scattering rates of phonons on two-level systems in disordered trigonal and hexagonal crystals. We apply a model in which the two-level system, characterized by a direction in space, is coupled to the strain field of the phonon via a tensor of coupling constants. The structure of the tensor of coupling constants is similar to the structure of the tensor of elastic stiffness constants, in the sense that they are determined by the same symmetry transformations. In this way, we emphasize the anisotropy of the interaction of elastic waves with the ensemble of two-level systems in disordered crystals. We also point to the fact that the ratio $\gamma_l/\gamma_t$ has a much broader range of allowed values in disordered crystals than in isotropic solids.