Dirac cones beyond the honeycomb lattice: a symmetry based approach

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.

arXiv comment9 pages, 8 figures, and 1 table

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• Observation of topological edge states of sound at a momentum away from the high-symmetry point
• Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Anisotropic effects in two-dimensional materials
• Peculiar bonding associated with atomic doping and hidden honeycombs in borophene
• Dirac-semimetal phase diagram of two-dimensional black phosphorus
• Twelve Inequivalent Dirac Cones in Two-Dimensional ZrB2
• Interplay between p- and d- orbitals yields multiple Dirac states in one- and two-dimensional CrB4
• Lattice symmetries and the topological protected transport of colloidal particles
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• Rapid Exploration of Topological Band Structures using Deep Learning
• Observation of Gapped Dirac Cones in a Two-Dimensional Su-Schrieffer-Heeger Lattice
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• Deformation induced pseudo-magnetic fields in complex carbon architectures
• Two-dimensional boron on Pb (110) surface
• Evolution from Topological Dirac Metal to Flat-band-Induced Antiferromagnet in Layered KxNi4S2 (0<=x<=1)
• Quantized Berry winding from an emergent $\mathcal{P}\mathcal{T}$ symmetry