Breakdown of universality in three-dimensional Dirac semimetals with random impurities

TL;DR

This paper demonstrates that rare impurity configurations in 3D Dirac semimetals can induce a transition from a semimetal to a compressible metal, challenging the assumed robustness of their electronic properties.

Contribution

It reveals how disorder statistics and impurity diversity critically affect the stability of 3D Dirac semimetals, highlighting the role of rare localized modes.

Findings

Rare impurity configurations create low-energy resonances.

These resonances lead to a finite density of states at zero energy.

The semimetal becomes a compressible metal even at low impurity densities.

Abstract

Dirac-Weyl semimetals are unique three-dimensional (3D) phases of matter with gapless electrons and novel electrodynamic properties believed to be robust against weak perturbations. Here, we unveil the crucial influence of the disorder statistics and impurity diversity in the stability of incompressible electrons in 3D semimetals. Focusing on the critical role played by rare impurity configurations, we show that the abundance of low-energy resonances in the presence of diluted random potential wells endows rare localized zero-energy modes with statistical significance, thus lifting the nodal density of states. The strong nonperturbative effect here reported converts the 3D Dirac-Weyl semimetal into a compressible metal even at the lowest impurity densities. Our analytical results are validated by high-resolution real-space simulations in record-large 3D lattices with up to 536 000 000 orbitals.