Novel topological phases of a semi-Dirac Chern insulator in presence of extended range hopping

Abstract

We study topological properties and the topological phase transitions therein for a semi-Dirac Haldane model on a honeycomb lattice in presence of an extended range (third neighbour) hopping. While in the absence of a third neighbour hopping, $t_3$, the system exhibits gapless electronic spectrum, its presence creates an energy gap in the dispersion. However, the nature of the spectral gap, that is, whether it is trivial or topological needs to be ascertained. We find that the answer depends on the value of $t_3$, and its interplay with the value of the onsite potential that breaks the sublattice symmetry, namely, Semenoff mass ($\Delta$). To elucidate our findings on the topological phases, we demonstrate two kinds of phase diagrams using the available parameter space, one in which the phases are shown in the $\Delta$-$t_3$ plane, and the other one in a more familiar $\Delta$-$\varphi$ plane ($\varphi$ being the Haldane flux). The phase diagrams depict the presence of Chern insulating lobes comprising of Chern numbers $\pm 2$ and $\pm 1$ for certain values of $t_3$, along with trivial insulating regions (zero Chern number). Thus there are phase transitions from one topological regime to another which are characterized by abrupt changes in the values of the Chern number. To support the existence of the topological phases, we compute the counter-propagating chiral edge modes in a ribbon geometry. Finally, the anomalous Hall conductivity shows plateaus either at $e^2/h$ or $2e^2/h$ corresponding to these topological phases.

References in corpus (37)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Topological Insulator Materials
• Strain-induced gap modification in black phosphorus
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Phase coexistence and metal-insulator transition in few-layer phosphorene: A computational study
• Merging of Dirac points in a two-dimensional crystal
• High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
• Half-metallic semiDirac point generated by quantum confinement in TiO${}_2$/VO${}_2$ nanostructures
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• Toward a realistic description of multilayer black phosphorus: from $GW$ approximation to large-scale tight-binding simulations
• Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
• The microscopic nature of localization in the quantum Hall effect
• Quantum Anomalous Hall Effect with Higher Plateaus
• Topological flat band models with arbitrary Chern numbers
• Tuning Chern Number in Quantum Anomalous Hall Insulators
• The insulator/Chern-insulator transition in the Haldane model
• Anomalous Hall effect in paramagnetic two dimensional systems
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
• Distant-Neighbor Hopping in Graphene and Haldane Models
• Photoinduced Chern insulating states in semi-Dirac materials
• Laser-induced topological transitions in phosphorene with inversion symmetry
• Metal-insulator transition through a semi-Dirac point in oxide nanostructures: VO${}_2$ (001) layers confined within TiO${}_2$
• Unconventional phases in a Haldane model of dice lattice
• Semi-Dirac Semimetal in Silicene Oxide
• Realizing Haldane Model in Fe-based Honeycomb Ferromagnetic Insulators
• Dirac point metamorphosis from third-neighbor couplings in graphene
• Lattice symmetries, spectral topology and opto-electronic properties of graphene-like materials
• Quantum Hall studies of a Semi-Dirac Nanoribbon
• Eight fold quantum Hall phases in a time reversal symmetry broken tight binding model
• Topological phase transition induced by band structure modulation in a Chern insulator
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Generating and detecting topological phases with higher Chern number

Cited by in corpus (6)

• Topological features of Haldane model on a dice lattice: role of flat band on transport properties
• Nonlinear magnetotransport in a two-dimensional system with merging Dirac points
• Band engineered bilayer Haldane model: Evidence of multiple topological phase transitions
• Extended Haldane Model in The Dice Lattice: Multiple Flat-Band-Induced topological Transitions Revealed
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Interacting type-II semi-Dirac quasiparticles