Symmetry Enforced Stability of Interacting Weyl and Dirac Semimetals

Abstract

The nodal and effectively relativistic dispersion featuring in a range of novel materials including two- dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anti-commutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

5 pages, 1 figure. In this revision we have clarified how the systems remain gapless

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• The electronic properties of graphene
• Titanic Magnetoresistance in WTe2
• The electronic properties of bilayer graphene
• Dirac materials
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Theory of interacting electrons on the honeycomb lattice
• Quantum transport in Dirac materials: signatures of tilted and anisotropic Dirac and Weyl cones
• Unconventional localisation transition in high dimensions
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• Stability of Dirac Liquids with Strong Coulomb Interaction
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Cited by in corpus (8)

• Unpaired Weyl nodes from Long-Ranged Interactions: Fate of Quantum Anomalies
• Breakdown of universality in three-dimensional Dirac semimetals with random impurities
• Non-Local Annihilation of Weyl Fermions in Correlated Systems
• Strongly Interacting Weyl Semimetals: Stability of the Semimetallic Phase and Emergence of Almost Free Fermions
• Manifestation of topological behaviors in interacting Weyl systems: one-body verse two-body correlations
• Fate of Fermi-arc States in Gapped Weyl Semimetals under Long-ranged Interactions
• Correlations in non-Hermitian systems and Diagram techniques for the steady state
• Spin density wave order in interacting type-I and type-II Weyl semimetals