Randomness Models of Dilute Impurities Determine the Fate of Quantum-Criticality in 3D Dirac Semimetals*

Nodal 3D electron gases have received renewed attention in recent years with the discovery of Dirac-Weyl semimetals. An outstanding issue is the lift of the nodal density of states (NDoS) by weak disorder. A semimetal-to-metal transition was expected at finite disorder, but recent analytical/numerical work [1] had contradictory conclusions swinging between this scenario and an “avoided quantum-criticality” one.
Combining analytical methods and high-resolution large-scale simulations [2], we show that scalar impurities can indeed endow a finite NDoS to a 3D semimetal, at infinitesimal concentrations. Concretely, a semimetal is unstable if the potential landscape has wells close to fine-tuned ’magical values’ hosting bound states. These newly unveiled near-critical configurations generate low-energy resonances, which give zero-energy modes statistical weight and lead to a diffusive metal [3]. Our simulations confirm this scenario, pointing vanishing size and multi-impurity effects as relevant to generalize these results to disordered lattices.
[1] PRB 89, 245110; PRL 121, 215301; PRX 6, 021042
[2] R. Soc. Open Sci. 7, 191809
[3] arXiv:2010.04998