We explore the topological properties of a modified Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor hopping terms is made unequal and the threefold rotational symmetry ${\mathcal{C}}_3$ is broken by introducing a dimerization term ($|t_{1w\left(2w\right)}|<t_{1s\left(2s\right)}$) in the Hamiltonian. Using the parameter $\eta =t_{1w}/t_{1s}=t_{2w}/t_{2s}$, we show that this MHM supports a transition from the quantum anomalous Hall insulator to a higher-order topological insulator (HOTI) phase at $\eta =\pm 0.5$. It also hosts a zero-energy corner mode on a nanodisk 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. Our MHM offers a rich tapestry of HOTIs and other topological and nontopological phases.

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• Anomalous Hall effect
• Electronic structure
• Topological materials