A typical medium cluster approach for multi-branch phonon localization

TL;DR

This paper extends a cluster approximation method to study how multiple phonon branches affect Anderson localization, revealing that the vector nature of phonons has minimal impact on the localization transition.

Contribution

The paper develops a multi-branch TMDCA formalism to analyze phonon localization, expanding previous single-branch models and validating against exact results.

Findings

Vector nature of phonons does not significantly influence Anderson transition.

Multi-branch TMDCA accurately models phonon spectra and localization.

Formalism can be applied to real material studies.

Abstract

The phenomenon of Anderson localization in various disordered media has sustained significant interest over many decades. Specifically, the Anderson localization of phonons has been viewed as a potential mechanism for creating fascinating thermal transport properties in materials. However, despite extensive work, the influence of the vector nature of phonons on the Anderson localization transition has not been well explored. In order to achieve such an understanding, we extend a recently developed phonon dynamical cluster approximation (DCA) and its typical medium variant (TMDCA) to investigate spectra and localization of multi-branch phonons in the presence of pure mass disorder. We validate the new formalism against several limiting cases and exact diagonalization results. A comparison of results for the single-branch versus multi-branch case shows that the vector nature of the phonons does not affect the Anderson transition of phonons significantly. The developed multi-branch TMDCA formalism can be employed for studying phonon localization in real materials.