Localization of a disordered phonon system: Anderson localization of optical phonons in AlxGa1-xAs

Localization properties of an isotopically disordered phonon system are studied by mapping the system to an electronic tight-binding problem with on-site disorder. When the model parameters are adjusted for the AlxGa1-xAs alloys, it is shown that there exists x(c) such that for x>x(c), all GaAs-like optical-phonon states are localized while for x<x(c), most states are extended except for some near the edges of the GaAs-like branch. These results are confirmed by an independent numerical investigation of the scaling behavior of the localization lengths. Our results reconcile current controversy regarding the nature of GaAs-like optical-phonon eigen states in the AlxGa1-xAs alloys