Abstract
We studied a non-interacting Λ/V-type dice model composed of three triangular sublattices. By considering the isotropic nearest-neighbor hoppings and the next-nearest-neighbor hoppings with the phase, as well as the quasi-staggered on-site potential, we acquired the full phase diagrams under the different fillings of the energy bands. There are abundant topological non-trivial phases with different Chern numbers C=±1, as well as higher ones ±2,±3 and a metal phase in several regimes. In addition, we also checked the bulk–edge correspondence of the system by analyzing the edge-state energy spectrum.
Highlights
In 1988, Haldane first theoretically pioneered the idea of breaking the time-reversal symmetry by applying a zero net magnetic flux through each unit cell in a hexagonal lattice and engineered a topological nontrivial model with C = ±1, which is known as the Haldane model [16]
We study the band structures of the model described by Equation (1)
In the ∆-φ parameter space, the system can be divided into two parts: parts: the metal phase and the bulk insulating phase
Summary
In 1988, Haldane first theoretically pioneered the idea of breaking the time-reversal symmetry by applying a zero net magnetic flux through each unit cell in a hexagonal lattice and engineered a topological nontrivial model with C = ±1, which is known as the Haldane model [16] This model opens a gate for people to study QAHE and has more or less influenced other two-dimensional systems that appeared later, such as the Checkerboard lattice [17], Kagomé lattice [18,19,20,21] and Lieb lattice [22,23,24,25].
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