Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant

TL;DR

This paper introduces a new higher-order topological insulator model based on the martini lattice, demonstrating in-gap corner states protected by a non-trivial topological invariant, and explores a square-root variant derived from a decorated honeycomb lattice.

Contribution

It proposes the martini lattice as a concrete example of higher-order topological insulators and introduces a square-root higher-order topological insulator based on a decorated honeycomb lattice.

Findings

In-gap corner states appear at finite energies.

Corner states are protected by a non-trivial bulk  topological invariant.

The models demonstrate higher-order topology in the proposed lattice structures.

Abstract

Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice model with two-site decoration, whose squared Hamiltonian consists of two martini lattice models, realizes square-root higher-order topological insulators. We show, for both of these two models, that in-gap corner states appear at finite energies and that they are portected by non-trivial bulk $\mathbb{Z}_3$ topological invariant.