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.

9 pages, 8 figures, and 1 table

References in corpus (13)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Epitaxial Growth of Two-Dimensional Stanene
• Germanene: a novel two-dimensional Germanium allotrope akin to Graphene and Silicene
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Electric Field Induced Topological Phase Transition in Two-Dimensional Few-layer Black Phosphorus
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Merging of Dirac points in a two-dimensional crystal
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry
• Massless Dirac Fermions in a Square Optical Lattice
• Tight-binding theory of spin-orbit coupling in graphynes
• High-Chern-number bands and tunable Dirac cones in $\beta$-graphyne

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• Symmetry-protected multifold exceptional points and their topological characterization
• Observation of topological edge states of sound at a momentum away from the high-symmetry point
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• 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
• Cat's cradle-like Dirac semimetals in layer groups with multiple screw axes: Application to 2D Borophene and Borophane
• Rapid Exploration of Topological Band Structures using Deep Learning
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• Double Dirac Cones and Topologically Non-Trivial Phonons for Continuous, Square Symmetric (C${}_{4v}$ and C${}_{2v}$) Unit Cells
• Dirac cones in Two-dimensional Borane
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Pyramids and cootie catchers: new massless fermions in 2D materials
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Topological obstructed atomic limit by annihilating Dirac fermions
• Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal
• Strong anisotropic optical properties of 8-Pmmn borophene: a many-body perturbation study
• 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