Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

Abstract

We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on ${\text{p}}_x$ and \emph{p}_{y} orbitals exhibit very interesting doubly degenerate energy points at different positions ($\Gamma$ and K/K${}^{\prime }$) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the $\Gamma$ and K/K${}^{\prime }$ points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of 2D triangular lattice metal-organic framework of Co(C${}_{21}$N${}_3$H${}_{15}$) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

11 pages, 5 figures

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• Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors -- A Perspective Review
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• Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2
• Chern insulators and high Curie temperature Dirac half-metal in two-dimensional metal-organic frameworks
• Designing Xenes with Two-Dimensional Triangular Lattice