Topological phase diagram of the Haldane model on a Bishamon-kikko–honeycomb lattice

We investigate the fundamental topological nature of electrons on a periodically $1/6$-depleted honeycomb lattice, which we call the Bishamon-kikko lattice after a Japanese traditional pattern, by adopting the Haldane model and comprehensively calculating the band structure and topological phase diagram. We also extend our study to the model connecting the Bishamon-kikko and honeycomb lattices. We show that these models exhibit richer topological characteristics compared to the original Haldane model on the honeycomb lattice, such as topological insulating states with higher Chern numbers, metallic states with nontrivial band topology even at commensurate electron fillings, and metal-insulator transitions between them. Our findings offer a playground of correlated topological phenomena and stimulate their realization in a variety of two-dimensional systems, such as van der Waals materials, graphene nanostructures, and photonic crystals.