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 (90)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Atomically thin MoS2: A new direct-gap semiconductor
• Experimental Observation of Quantum Hall Effect and Berry's Phase in 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
• Two and one-dimensional honeycomb structures of silicon and germanium
• Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2
• Quantum Spin Hall Effect in Silicene
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
• Epitaxial Growth of a Silicene Sheet
• Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
• A tight-binding approach to uniaxial strain in graphene
• Cloning of Dirac fermions in graphene superlattices
• Large-gap quantum spin Hall insulators in tin films
• Evidence of silicene in honeycomb structures of silicon on Ag(111)
• First-principles study of the interaction and charge transfer between graphene and metals
• A self-consistent theory for graphene transport
• Electrically Tunable Band Gap in Silicene
• Properties of Graphene: A Theoretical Perspective
• All-graphene integrated circuits via strain engineering
• Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene
• Observation of the Fractional Quantum Hall Effect in Graphene
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Evidence for Dirac Fermions in a honeycomb lattice based on silicon
• Origin of Spatial Charge Inhomogeneity in Graphene
• Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field
• Effects of Strain on Electronic Properties of Graphene
• Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions
• 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
• Gated Silicene as a tunable source of nearly 100% spin-polarized electrons
• Artificial graphene as a tunable Dirac material
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Graphyne: Hexagonal network of carbon with versatile Dirac cones
• Valley-Polarized Quantum Anomalous-Hall Effects in Silicene
• Limits on electron quality in suspended graphene due to flexural phonons
• Merging of Dirac points in a two-dimensional crystal
• Growth of silicene layers on Ag(111): unexpected effect of the substrate temperature
• Midgap states and charge inhomogeneities in corrugated graphene
• Negative Refraction and Left-handed electromagnetism in Microwave Photonic Crystals
• 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
• Existence and topological stability of Fermi points in multilayered graphene
• Half-metallic semiDirac point generated by quantum confinement in TiO${}_2$/VO${}_2$ nanostructures
• Zero modes of tight binding electrons on the honeycomb lattice
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Merging of Dirac points and Floquet topological transitions in AC driven graphene
• Engineering artificial graphene in a two-dimensional electron gas
• On the electronic structure of silicene on Ag substrate: strong hybridization effects
• Topological transition of Dirac points in a microwave experiment
• The energy landscape of fullerene materials: a comparison between boron, boron-nitride and carbon
• Electron-Phonon Interactions and the Intrinsic Electrical Resistivity of Graphene
• Barrier transmission of Dirac-like pseudospin-one particles
• Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
• Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases
• Silicene Structures on Silver Surfaces
• Effects of the Zero-Mode Landau Level on Inter-Layer Magnetoresistance in Multilayer Massless Dirac Fermion Systems
• A Gapless MoS${}_2$ Allotrope Possessing Both Massless Dirac and Heavy Fermions
• Fractional Quantum Hall Phase Transitions and Four-flux Composite Fermions in Graphene
• Semi-Dirac dispersion relation in photonic crystals
• Emergent topological and half semimetallic Dirac Fermions at oxide interfaces
• Unusual ultralow frequency fluctuations in freestanding graphene
• Strain-induced Dirac cone-like electronic structures and semiconductor-semimetal transition in graphdiyne
• Designing Dirac points in two-dimensional lattices
• Absence of Dirac Electrons in Silicene on Ag (111) Surfaces
• Revealing the substrate origin of the linear dispersion of silicene/Ag(111)
• From laterally modulated two-dimensional electron gas towards artificial graphene
• Quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi${}_2$
• Strong Band Hybridization between Silicene and Ag(111)Substrate
• Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions: Application to Fermionic Shastry-Sutherland Model
• Tight-binding theory of spin-orbit coupling in graphynes
• Designer Topological Insulators in Superlattices
• Topological aspect of graphene physics
• 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
• R-graphyne: a new two-dimension carbon allotrope with versatile Dirac-like point in nanoribbons

Cited by in corpus (85)

• Phagraphene: A Low-energy Graphene Allotrope composed of 5-6-7 Carbon Rings with Distorted Dirac Cones
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Dirac fermions in borophene
• Mobility anisotropy of two-dimensional semiconductors
• Synthesis of a mesoscale ordered 2D-conjugated polymer with semiconducting properties
• Model for Topological Phononics and Phonon Diode
• Strain-induced pseudomagnetic field in Dirac semimetal borophene
• Highly Itinerant Atomic Vacancies in Phosphorene
• Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications
• Anisotropic carrier mobility of distorted Dirac cones: theory and application
• Two-dimensional Spin-Orbit Dirac Point in Monolayer HfGeTe
• Dirac points with giant spin-orbit splitting in the electronic structure of two-dimensional transition-metal carbides
• Oblique Klein tunneling in 8-Pmmn borophene p-n junctions
• Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure
• Optical properties of massive anisotropic tilted Dirac systems
• Metal-Insulator transition in 8-Pmmn Borophene under perpendicular incidence of electromagnetic radiation
• Generalized Dirac structure beyond the linear regime in graphene
• Semi-Dirac Semimetal in Silicene Oxide
• Monolayer Mg${}_2$C: Negative Poisson's ratio and unconventional 2D emergent fermions
• Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera
• A review of thermal transport and electronic properties of borophene
• Sensitive single-photon test of extended quantum theory with 2D hexagonal boron nitride
• Phonon helicity induced by electronic Berry curvature in Dirac materials
• Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points
• Optical absorption in two-dimensional materials with tilted Dirac cones
• Anomalous localization behaviors in disordered pseudospin systems: Beyond the conventional Anderson picture
• Confining massless Dirac particles in two-dimensional curved space
• Negative-curvature spacetime solutions for graphene
• Manipulation of exciton and trion quasiparticles in monolayer WS2 via charge transfer
• Anomalous caustics and Veselago focusing in 8-Pmmn borophene p-n junctions with arbitrary junction directions
• Granular Superconductor in a honeycomb lattice as a realization of Bosonic Dirac Material
• Strain-induced Weyl and Dirac states and direct-indirect gap transitions in group-V materials
• Observation of one-dimensional Dirac fermions in silicon nanoribbons
• Monolayer 2D semiconducting tellurides for high-mobility electronics
• Observation of Gapped Dirac Cones in a Two-Dimensional Su-Schrieffer-Heeger Lattice
• C${}_4$N${}_3$H monolayer: A novel two-dimensional organic Dirac material with high Fermi velocity
• Anomalous heat flow in 8-$Pmmn$ borophene with tilted Dirac cones
• Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices
• Graphene, Dirac equation and analogue gravity
• Magnetoresistance of a three-dimensional Dirac gas
• Anisotropic-cyclicgraphene: A new two-dimensional semiconducting carbon allotrope
• Two-dimensional Topological Semimetals Protected by Symmorphic Symmetries
• Valley-Selective Landau-Zener Oscillations in Semi-Dirac p-n Junctions
• Electronic transport in two-dimensional strained Dirac materials under multi-step Fermi velocity barrier: transfer matrix method for supersymmetric systems
• Quantum electrodynamics in anisotropic and tilted Dirac photonic lattices
• Electronic properties of silicene in BN/silicene van der Waals heterostructures
• Pyramids and cootie catchers: new massless fermions in 2D materials
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Parabolic Metamaterials and Dirac Bridges
• Existence of Dirac cones in Brillouin zone of diperiodic atomic crystals according to group theory
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Interacting Dirac Materials
• Decay of semiclassical massless Dirac fermions from integrable and chaotic cavities
• Veselago focusing of anisotropic massless Dirac fermions
• Quantum Spin Hall Effect and Su-Schrieffer-Heeger Model Implementation in Novel C3N-based Dumbbell Morphologies
• Polarizability, plasmons, and screening in 1T${}^{\prime }$-MoS${}_2$ with tilted Dirac bands
• Time-diffraction and Zitterbewegung of two-dimensional massless Dirac excitations
• Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects
• Proposal for a graphene based nano-electro-mechanical reference piezoresistor
• Generating extreme quantum scattering in graphene with machine learning
• Charge-pseudospin coupled diffusion in semi-Dirac graphene: pseudospin assisted valley transport
• Opacity of graphene independent of light frequency and polarization due to the topological charge of the Dirac points
• Roles of band gap and Kane electronic dispersion in the THz-frequency nonlinear optical response in HgCdTe
• Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields
• Strong anisotropic optical properties of 8-Pmmn borophene: a many-body perturbation study
• Electromagnetic properties of a double layer graphene system with electron-hole pairing
• A dynamical Toric Code model with fusion and de-fusion
• A simple rule for finding Dirac Cones in Bilayered Perovskites
• Landau Quantized Dynamics and Spectrum of the Diced Lattice
• The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model
• CUBIT: Capacitive qUantum BIT
• Tunable bandgaps and flat bands in twisted bilayer biphenylene carbon
• Cascade of phase transitions in a planar Dirac material
• Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals
• Microscopic Green's function approach for generalized Dirac Hamiltonians
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Dirac cones for a mean-field model of graphene
• Deformation induced pseudo-magnetic fields in complex carbon architectures
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system
• Protected Fermionic Zero Modes in Periodic Gauge Fields
• The perfect spin injection in silicene FS/NS junction
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Two-dimensional honeycomb-kagome V2O3: a robust room-temperature magnetic Chern insulator interfaced with graphene
• Holographic entanglement renormalisation for fermionic quantum matter
• Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions