# Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekul\'{e} Distortion

## TL;DR

This paper proposes a honeycomb-lattice model with anti-Kekulé distortion as a higher-order topological insulator, demonstrating its topological phase via Berry phase calculations and corner state analysis.

## Contribution

It introduces a new honeycomb-lattice model with anti-Kekulé distortion hosting higher-order topological phases, expanding the understanding of topological insulators.

## Key findings

- Existence of higher-order topological phase confirmed by Berry phase calculations.
- Presence of corner states indicating non-trivial topology.
- Anti-Kekulé pattern induces topological boundary states.

## Abstract

Higher-order topological insulators have attracted considerable interests as a novel topological phase of matter, where topologically non-trivial nature of bulk protects boundary states whose co-dimension is larger than one. It has been revealed that the alternating pattern of hopping amplitudes in two-dimensional lattices provides a promising route to realization of the higher-order topological insulators. In this paper, we propose that a honeycomb-lattice model with anti-Kekul\'{e} distortion hosts a higher-order topological phase. Here, the term anti-Kekul\'{e} distortion means that the pattern of strong and weak hoppings is opposite to that for the conventional Kekul\'{e} distortion. We demonstrate the existence of the higher-order topological phase by calculating the $\mathbb{Z}_6$ Berry phase that serves as a bulk topological invariant of the higher-order topological phase, and by showing the existence of corner states.