The Dirac-Weyl semimetal: Coexistence of Dirac and Weyl fermions in polar hexagonal $ABC$ crystals

TL;DR

This paper predicts a new topological semimetal phase in noncentrosymmetric hexagonal $ABC$ crystals, where Dirac and Weyl fermions coexist, and identifies candidate materials for experimental realization.

Contribution

It introduces the concept of a Dirac-Weyl semimetal phase in polar hexagonal $ABC$ crystals and provides first-principles analysis and a low-energy model for this phase.

Findings

Coexistence of Dirac and Weyl points in SrHgPb.

Identification of topological phase transition driven by layer buckling.

Proposal of SrHgSn and CaHgSn as candidate materials.

Abstract

We propose that the noncentrosymmetric LiGaGe-type hexagonal $ABC$ crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space. The symmetry-protected Dirac points arise due to a band inversion and are located on the sixfold rotation $z$-axis, whereas the six pairs of Weyl points related by sixfold symmetry are located on the perpendicular $k_z=0$ plane. By studying the electronic structure as a function of the buckling of the HgPb layer, which is the origin of inversion symmetry breaking, we establish that the coexistence of Dirac and Weyl fermions defines a phase separating two topologically distinct Dirac semimetals. These two Dirac semimetals are distinguished by the $\mathbb{Z}_2$ index of the $k_z=0$ plane and the corresponding presence or absence of 2D Dirac fermions on side surfaces. We formalize our first-principles calculations by deriving and studying a low-energy model Hamiltonian describing the Dirac-Weyl semimetal phase. We conclude by proposing several other materials in the non-centrosymmetric $ABC $ material class, in particular SrHgSn and CaHgSn, as candidates for realizing the Dirac-Weyl semimetal.