Anderson localization of phonons in multi-branch mass-disordered systems*

The Anderson localization (AL) of phonons in disordered media has been receiving increasing interest

due to potential impact on thermoelectric materials. However, despite extensive study, the influence of

the directional nature of phonons on the AL transition remains elusive. Recently, we have formulated the

typical medium cluster approach which allows to study the AL of phonons in multibranch systems.

Considering the model with three directions of lattice vibrations in the presence of mass disorder, we

have investigated the interplay of inter-branch mixing and diagonal disorder in the context of phonon

localization. We have validated the new formalism against several limiting cases and exact

diagonalization results. We have also contrasted the mechanism of AL for the single branch versus

multiple branch case, and elucidated the role of directional nature of phonon on AL.