Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice

Abstract

Moving, merging and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states is obtained to be $D(\epsilon )\propto |\epsilon {|}^{1/3}$ when three Dirac points merge, and $D(\epsilon )\propto |\epsilon {|}^{1/4}$ at the tricritical points. It is possible to realize these topological phase transitions in the ultracold atoms on the optical lattice, strained monolayer graphene or strained bilayer graphene.

19 pages, 25 figures

References in corpus (22)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Substrate-induced band gap opening in epitaxial graphene
• A tight-binding approach to uniaxial strain in graphene
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Quantum transport of massless Dirac fermions in graphene
• Effects of Strain on Electronic Properties of Graphene
• Merging of Dirac points in a two-dimensional crystal
• Gap opening in graphene by shear strain
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• Observation of Dirac Cone Electronic Dispersion in BaFe2As2
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• Comment on "Band structure engineering of graphene by strain: First-principles calculations"
• Effects of the Zero-Mode Landau Level on Inter-Layer Magnetoresistance in Multilayer Massless Dirac Fermion Systems
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Strained bilayer graphene: Band structure topology and Landau level spectrum
• Electronic topological transition in sliding bilayer graphene
• Electric Conductivity of the Zero-gap Semiconducting State in Alpha-(BEDT-TTF)2I3 Salt
• Dirac point metamorphosis from third-neighbor couplings in graphene
• Magnetic spectrum of trigonally warped bilayer graphene - semiclassical analysis, zero modes, and topological winding numbers

Cited by in corpus (13)

• Tight-binding couplings in microwave artificial graphene
• Topological Effects in Chiral Symmetric Driven Systems
• Double transfer through Dirac points in a tunable honeycomb optical lattice
• Tight binding models for ultracold atoms in honeycomb optical lattices
• Impurity bound states as detectors of topological band structures revisited
• Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Observing Movement of Dirac Cones from Single-Photon Dynamics
• Topological transitions in a model with Particle-Hole symmetry, Pancharatnam-Berry Curvature and Dirac Points
• Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems
• Dirac points merging and wandering in a model Chern insulator
• Merged Four Dirac Points at the Critical Interlayer Distance in Commensurately Twisted Bilayer Graphene: the Origin of the Zero Velocity
• Floquet-Engineered Valley-Topotronics in Kekulé-Y Bond Textured Graphene Superlattice