Dirac cones beyond the honeycomb lattice: a symmetry based approach

TL;DR

This paper classifies two-dimensional Dirac systems based on symmetry, revealing new materials with multiple Dirac cones and providing a unified framework beyond the honeycomb lattice, with implications for material engineering.

Contribution

It introduces a symmetry-based classification of Dirac materials, identifying novel systems with multiple Dirac cones and linking their emergence to mirror symmetries and minimal models.

Findings

Discovered materials with up to twelve inequivalent Dirac cones.

Linked Dirac cone emergence to mirror symmetries in the materials.

Provided a unified description for various 2D Dirac systems.

Abstract

Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on the space groups, and discuss our findings within the context of a minimal two-band model. In particular, we show that the emergence of massless Dirac fermions can be attributed to the mirror symmetries of the materials. Moreover, we uncover several novel Dirac systems that have up to twelve inequivalent Dirac cones, and show that these can be realized in (twisted) bilayers. Hereby, we obtain systems with an emergent SU(2N) valley symmetry with N=1,2,4,6,8,12. Our results pave the way to engineer different Dirac systems, besides providing a simple and unified description of materials ranging from square- and $\beta$-graphynes, to Pmmn-Boron, TiB$_2$, phosphorene, and anisotropic graphene.