Dirty Weyl fermions: rare region effects near 3D Dirac points

TL;DR

This paper investigates how rare region effects induce nonzero density of states and influence transport in 3D Dirac fermions with weak disorder, challenging previous assumptions of disorder irrelevance.

Contribution

It reveals nonperturbative rare region effects in 3D Dirac systems, showing they dominate low-energy properties and alter the understanding of disorder relevance.

Findings

Rare regions cause nonzero density of states at Dirac points.

Transport is dominated by hopping between rare regions.

Disorder can induce a transition to a granular superconductor or Bose glass.

Abstract

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. We show that even though disorder is perturbatively irrelevant at 3D Dirac points, nonperturbative effects from rare regions give rise to a nonzero density of states and a finite mean free path, with the transport at the Dirac point being dominated by hopping between rare regions. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We also discuss the interplay of disorder with interactions at the Dirac point. Attractive interactions drive a transition into a granular superconductor, with a critical temperature that depends strongly on the disorder distribution. In the presence of Coulomb repulsion and weak retarded attraction, the system can be a Bose glass. Our results apply to all 3D systems with Dirac points, including Weyl semimetals, and overturn a thirty year old consensus regarding the irrelevance of weak disorder at 3D Dirac points.