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.
Highlights
The discovery of Dirac and Weyl semimetals (DWSMs) has provided a rich arena for probing novel gapless phases of matter with unique transport properties and topological features [1]
We have shown that avoided quantum criticality (AQC) must occur in 3D Dirac semimetals having dilute short-range scalar impurities, if their random parameters have a nonzero probability density at so-called magical values, where nodal bound states appear
The perfect agreement between theory and numerical simulations gives confidence that the newly unveiled resonant mechanism stemming from diverse near-critical impurities is a crucial piece in the DWSM quantum criticality puzzle
Summary
The discovery of Dirac and Weyl semimetals (DWSMs) has provided a rich arena for probing novel gapless phases of matter with unique transport properties and topological features [1]. The early field-theoretical point of view has been recently questioned by nonperturbative calculations [20,24], hinting that 3D gapless phases can become unstable due to the emergence of zero-energy states bound to statistically rare regions of the disorder potential landscape According to this picture, the nodal DoS remains nonzero for arbitrarily weak disorder without any signature of singular behavior. Evidence for avoided quantum criticality (AQC) facilitated by localized nodal eigenstates has been provided by lattice simulations of a 3D Dirac model with uncorrelated on-site disorder [24] Challenging these findings, Buchhold et al noted that rare events are preceded by scattering resonances which always carry zero spectral weight at a node. VI we summarize our main findings and highlight future directions for further study
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