Interaction of two level systems in amorphous materials with arbitrary phonon fields

TL;DR

This paper generalizes the interaction Hamiltonian for two-level systems in amorphous materials, showing that the coupling with longitudinal phonons is generally stronger than with transverse phonons, based on a new tensor model.

Contribution

It introduces a tensor-based model for TLS-phonon interactions in amorphous solids, reducing to two key parameters due to isotropy, and relates these to experimental data.

Findings

Average TLS coupling with longitudinal phonons exceeds that with transverse phonons.

The model simplifies to two parameters for isotropic amorphous materials.

Experimental data can determine the two key deformation potential parameters.

Abstract

To describe the interaction of the two level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this new model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a $6\times 6$ symmetric tensor of deformation potential parameters, $[R]$. Taking into account the isotropy of the amorphous solid, we deduce that $[R]$ has only two independent parameters. We show how these two parameters can be calculated from experimental data and we prove that for any amorphous bulk material the average coupling of TLSs with longitudinal phonons is always stronger than the average coupling with transversal phonons (in standard notations, $\gamma_l>\gamma_t$).