Dirac cones beyond the honeycomb lattice: A symmetry-based approach.

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-dimensionalDirac 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 12 inequivalent Dirac cones and showthat 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, in addition to providing a simple and unified description of materials ranging from square and β-graphynes to Pmmn boron, TiB2, phosphorene, and anisotropic graphene. [ABSTRACT FROM AUTHOR]