A typical medium dynamical cluster approximation for studying Anderson localization of phonons in multi-branch mass-disordered systems

The phenomenon of Anderson localization (AL) has generated a lot of interest over many decades. Specifically, the AL of phonons has been viewed as a potential mechanism for improving the figure of merit of thermoelectric materials. Despite extensive work, the influence of the directional nature of phonons on the AL transition has not been well explored. In this talk, I will discuss the recently developed typical medium dynamical cluster approximation to investigate the AL of phonons considering three directions of lattice vibrations in the presence of mass disorder. We have validated the new formalism against several limiting cases and exact diagonalization results. A comparison of results for the single branch versus multiple branch case yields several interesting observations of the interplay of inter-branch mixing and diagonal disorder in the context of phonon localization.