# Non-trivial Topological Phases on the Stuffed Honeycomb Lattice

## TL;DR

This paper explores the emergence of nontrivial topological phases, including Chern insulators, in a modified honeycomb lattice model with complex hopping terms, revealing new topological states and phase transitions.

## Contribution

It introduces a new topological phase in a stuffed honeycomb lattice model with an added basis, expanding the understanding of topological phases in lattice systems.

## Key findings

- Identification of Chern insulating and semi-metallic phases
- Existence of topologically protected edge states
- Additional topological phase with Chern number ±2

## Abstract

We report the appearance of nontrivial topological phases in a tight-binding model on the stuffed honeycomb lattice. The model contains nearest neighbor and next nearest neighbor hopping terms coupled with an additional phase depending on the direction of hopping. Chern insulating and semi-metallic phases emerge with the change of hopping parameters. Nonzero Chern numbers characterizing the bands and the existence of topologically protected edge states in the gap between the relevant bands confirm the presence of those phases. We show that adding an extra basis to Haldane's honeycomb model can lead to an additional topological phase characterized by Chern number $\pm2$. Transition between different topological phases driven by the hopping parameters has been illustrated in the topological phase diagram of the system. Zero temperature Hall conductivity along with density of states is evaluated. Topological properties of another tight-binding model on the stuffed square lattice are also reported in this article.