Symmetry Enforced Stability of Interacting Weyl and Dirac Semimetals

TL;DR

This paper demonstrates that the nodal points in Weyl and Dirac semimetals are perturbatively stable against interactions due to specific symmetries, with implications for the robustness of their electronic properties.

Contribution

It provides a symmetry-based proof of the perturbative stability of Weyl and Dirac points in various materials, extending understanding of their robustness.

Findings

Nodal points are perturbatively stable to all orders due to anti-commuting spatial symmetries.

Stability applies to single and multilayer graphene, Weyl, and Dirac semimetals.

Certain Hamiltonians can acquire gaps from interactions when different symmetries are involved.

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.