Rare region effects across a topological to trivial insulator quantum phase transition in three-dimensions

We revisit whether the disorder driven phase transition between trivial and topological insulators in three-dimensions remains a semimetal at weak disorder. While the (clean) Dirac semimetallic critical point is perturbatively stable, non-perturbative effects of rare regions have recently been shown to destabilize the semimetal phase by creating a finite density of states. This implies that an intervening diffusive metal phase may develop that has been overlooked in previous studies. We apply the kernel polynomial method to numerically calculate transport properties on large system sizes to determine the stability of this putative semimetal phase boundary. A qualitative picture of transport through tunneling between rare regions will be put forth.