The transition from fracton to phonon states in a Sierpinski triangle lattice

Lattice dynamics of a Sierpinski triangle submitted to different levels of disorder was studied via atomistic Green’s functions. It was found that there is a critical level of disorder that separates two regions of thermal transport. The first is characterized by a fast destruction of fracton states and the formation of spatially extended phonon states. The second region is characterized by a transition from extended to localized phonon states as predicted by the Anderson model.

Research highlights► A Sierpinski triangle was studied with different self-similarity levels and disorder. ► A transition from fracton to phonon states was observed for low disorder. ► A second transition was observed from extended to localized phonon states. ► The transitions correspond to a change in topology in the average density of states.