Extended Fractons and Localized Phonons on Percolation Clusters

TL;DR

This paper studies vibrational mode localization in percolation clusters, revealing that all states are localized in 2D and identifying a novel transition to extended fracton states in 3D.

Contribution

It uncovers a new regime of extended fracton states in 3D percolation clusters, challenging previous assumptions about phonon localization.

Findings

All eigenstates are localized in 2D clusters.

Evidence of a localization-delocalization transition in 3D.

Discovery of a regime of extended fracton states above the phonon crossover.

Abstract

We investigate the localization behavior of vibrational modes of infinite percolation clusters above the critical concentration in two and three dimensions using the method of level statistics. We find that all eigenstates are localized in d=2, including the low frequency phonon states. In d=3 we obtain evidence for a localization-delocalization transition. But contrary to the common view this transition occurs for frequencies above the phonon fracton crossover giving rise to a new regime of extended fracton states.