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

TL;DR

This paper explores the topological states in 2D triangular lattices with multi-orbitals, revealing how interference effects influence topological phases and predicting a Chern insulator in a specific metal-organic framework.

Contribution

It demonstrates how interference effects suppress topological states in 2D triangular lattices and proposes a method to induce topological nontriviality via lattice coupling, supported by first-principles calculations.

Findings

Identification of doubly degenerate energy points with quadratic and linear dispersions.

Discovery of a destructive interference effect leading to trivial topological states.

Prediction of intrinsic Chern insulating behavior in a metal-organic framework.

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 $\emph{p}_{x}$ 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.