Band engineered bilayer Haldane model: Evidence of multiple topological phase transitions

Abstract

We have studied the evolution of the topological properties of a band-engineered AB-stacked bilayer honeycomb structure in the presence of a Haldane flux. Without a Haldane flux, band engineering makes the band touching points (the so-called Dirac points) move towards each other and eventually merge into one at an intermediate $\mathbf{M}$ point in the Brillouin zone. Here the dispersion is linear along one direction and quadratic along the other. In the presence of a Haldane flux, the system acquires topological properties, and finite Chern numbers can be associated with the pairs of the conduction and the valence bands. The valence band closer to the Fermi level ($E_F$) possesses Chern numbers equal to $\pm 2$ and $\pm 1$, while the one further away from $E_F$ corresponds to Chern numbers $\pm 1$. The conduction bands are associated with similar properties, except their signs are reversed. The Chern lobes shrink in the band-engineered model, and we find evidence of multiple topological phase transitions, where the Chern numbers discontinuously jump from $\pm 2$ to $\mp 2$, $\pm 1$ to $\mp 1$, $\pm 1$ to $0$ to $\pm 2$ and $\pm 2$ to $\pm 1$. These transitions are supported by the presence or absence of the chiral edge modes in a nanoribbon bilayer geometry and the vanishing of the plateau in the anomalous Hall conductivity. Different phases are further computed for different hopping amplitudes across the layers, which shows the shrinking of the Chern lobes for large interlayer tunneling.

References in corpus (27)

• Berry Phase Effects on Electronic Properties
• 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
• High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
• Topological mosaic in Moiré superlattices of van der Waals heterobilayers
• Half-metallic semiDirac point generated by quantum confinement in TiO${}_2$/VO${}_2$ nanostructures
• Zero modes of tight binding electrons on the honeycomb lattice
• Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
• Quantum Anomalous Hall Effect with Higher Plateaus
• Topological flat band models with arbitrary Chern numbers
• Tuning Chern Number in Quantum Anomalous Hall Insulators
• 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
• Metal-insulator transition through a semi-Dirac point in oxide nanostructures: VO${}_2$ (001) layers confined within TiO${}_2$
• Semi-Dirac Semimetal in Silicene Oxide
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Topological proximity effects in a Haldane-graphene bilayer system
• Topological features of Haldane model on a dice lattice: role of flat band on transport properties
• Novel topological phases of a semi-Dirac Chern insulator in presence of extended range hopping
• 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
• Bulk topological proximity effect in multilayer systems
• Vanishing of the quantum spin Hall phase in a semi-Dirac Kane Mele model
• Bilayer Haldane model: From trivial band insulator to fractionalized quantum anomalous Hall insulator

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