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

TL;DR

This paper explores the topological phase diagram of the Haldane model on a novel Bishamon-kikko honeycomb lattice, revealing richer topological states and transitions than the original model, with implications for 2D materials and photonic systems.

Contribution

It introduces the Haldane model on the Bishamon-kikko lattice, uncovering new topological phases and transitions not present in the standard honeycomb lattice.

Findings

Higher Chern number topological insulators identified

Metallic states with nontrivial topology at specific fillings

Metal-insulator transitions between topological phases

Abstract

Topological flat bands have gained extensive interest as a platform for exploring the interplay between nontrivial band topology and correlation effects. In recent studies, strongly correlated phenomena originating from a topological flat band were discussed on a periodically 1/6-depleted honeycomb lattice, but the fundamental topological nature associated with this lattice structure remains unexplored. Here we study the band structure and topological phase diagram for the Haldane model on this lattice, which we call the Bishamon-kikko lattice. 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.7 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.