A Higher-Order Topological Insulator Phase in a Modulated Haldane Model

TL;DR

This paper investigates a modulated Haldane model that exhibits a transition from a quantum anomalous Hall insulator to a higher-order topological insulator with corner modes, revealing new topological phases and transitions driven by symmetry breaking.

Contribution

It introduces a modulated Haldane model with broken rotational symmetry that supports a HOTI phase and characterizes the topological phase transitions and corner states.

Findings

Supports transition from QAHI to HOTI at specific parameter values

Hosts zero-energy corner modes that can be trivialized without gap closing

Features magnetic semimetal states with movable Dirac nodes

Abstract

We explore topological properties of a modulated Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor terms is made unequal and the three-fold rotational symmetry $\mathcal{C}_3$ is broken by introducing a trimerization term ($|t_{1w(2w)}|< t_{1s(2s)}$) in the Hamiltonian. Using the parameter $\eta={t_{1w}}/{t_{1s}}= t_{2w}/t_{2s}$, we show that the MHM supports a transition from the quantum anomalous Hall insulator (QAHI) to a HOTI phase at $\eta=\pm 0.5$. The MHM also hosts a zero-energy corner mode on a nano-disk that can transition to a trivial insulator without gap-closing when the inversion symmetry is broken. The gap-closing critical states are found to be magnetic semimetals with a single Dirac node which, unlike the classic Haldane model, can move along the high-symmetry lines in the Brillouin zone. MHM offers a rich tapestry of HOTI and other topological and non-topological phases.