Introduction to Dirac materials and topological insulators

Abstract

We present a short pedagogical introduction to the physics of Dirac materials, restricted to graphene and two- dimensional topological insulators. We start with a brief reminder of the Dirac and Weyl equations in the particle physics context. Turning to condensed matter systems, semimetallic graphene and various Dirac insulators are introduced, including the Haldane and the Kane-Mele topological insulators. We also discuss briefly experimental realizations in materials with strong spin-orbit coupling.

24 pages, 8 figures; review submitted to topical issue of "Comptes Rendus de l'Académie des Sciences (Physique)" devoted to topological insulators and Dirac matter. Pre-publication version; comments are invited

References in corpus (30)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Chiral tunneling and the Klein paradox in graphene
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Dissipationless Quantum Spin Current at Room Temperature
• Photovoltaic Hall effect in graphene
• High temperature fractional quantum Hall states
• Quantum interference and Klein tunneling in graphene heterojunctions
• Fractional quantum Hall states at zero magnetic field
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Nearly-flat bands with nontrivial topology
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Transport measurements across a tunable potential barrier in graphene
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Artificial graphene as a tunable Dirac material
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases
• Contact resistance and shot noise in graphene transistors
• Anomalous Edge Transport in the Quantum Anomalous Hall State

Cited by in corpus (47)

• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• A Materials Perspective on Casimir and van der Waals Interactions
• Model for Topological Phononics and Phonon Diode
• Topological and geometrical aspects of band theory
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Coupling of magnetic order to planar Bi electrons in the anisotropic Dirac metals AMnBi2 (A = Sr, Ca)
• Topological carbon materials: a new perspective
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors -- A Perspective Review
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• The Casimir effect in topological matter
• Lattice-layer entanglement in Bernal-stacked bilayer graphene
• Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials
• Topological proximity effects in a Haldane-graphene bilayer system
• Evolution of magnetic Dirac bosons in a honeycomb lattice
• Intense-pulse dynamics of massless Dirac electrons
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity
• $SU(2)\otimes SU(2)$ bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions
• Multiple solutions for a self-consistent Dirac equation in two dimensions
• Graphene lattice-layer entanglement under non-Markovian phase noise
• Topology of 2D Dirac operators with variable mass and an application to shallow-water waves
• Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems
• Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall
• Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation
• Anomalous quantum Hall effect induced by disorder in topological insulators
• Strong Correlation, Bloch Bundle Topology and Spinless Haldane-Hubbard Model
• Spontaneous emission of a quantum emitter near a Chern insulator: interplay of time reversal symmetry breaking and van Hove singularity
• Observation of topological valley Hall edge states in honeycomb lattices of superconducting microwave resonators
• One-dimensional scattering of fermions in double Dirac delta potentials
• 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
• Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals
• Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description
• Semimetallic and semiconducting graphene-hBN multilayers with parallel or reverse stacking
• Topological insulators and geometry of vector bundles
• Twin Domain Structure in Magnetically Doped Topological Insulators
• Quantum Hall and Light Responses in a 2D Topological Semimetal
• Two-dimensional Dirac matter in the semiclassical regime
• On 3D and 1D Weyl particles in a 1D box
• Understanding the magnetic interactions of the zig-zag honeycomb lattice: Application to $\alpha$-RuCl${}_3$
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Holographic entanglement renormalisation for fermionic quantum matter
• Exactly-solvable quantum systems in terms of Lambert-W functions
• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators
• Landau levels of a Dirac electron in graphene from non-uniform magnetic fields
• Transport of Dirac magnons driven by gauge fields