The Rare Two-Dimensional Materials with Dirac Cones

Abstract

Inspired by the great development of graphene, more and more works have been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann-Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.

Review paper, 31 pages, 10 figures

References in corpus (32)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Ultrahigh electron mobility in suspended graphene
• Boron nitride substrates for high-quality graphene electronics
• The structure of suspended graphene sheets
• Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer
• Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2
• A tight-binding approach to uniaxial strain in graphene
• A self-consistent theory for graphene transport
• All-graphene integrated circuits via strain engineering
• Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene
• Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene
• Multicomponent fractional quantum Hall effect in graphene
• Limits on electron quality in suspended graphene due to flexural phonons
• Merging of Dirac points in a two-dimensional crystal
• Midgap states and charge inhomogeneities in corrugated graphene
• Group-IV graphene- and graphane-like nanosheets
• Organic Topological Insulators in Organometallic Lattices
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Zero modes of tight binding electrons on the honeycomb lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Engineering artificial graphene in a two-dimensional electron gas
• Electron-Phonon Interactions and the Intrinsic Electrical Resistivity of Graphene
• Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases
• Effects of the Zero-Mode Landau Level on Inter-Layer Magnetoresistance in Multilayer Massless Dirac Fermion Systems
• Unusual ultralow frequency fluctuations in freestanding graphene
• Revealing the substrate origin of the linear dispersion of silicene/Ag(111)
• Tight-binding theory of spin-orbit coupling in graphynes
• High-Chern-number bands and tunable Dirac cones in $\beta$-graphyne
• Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid