Topological Corner States on Kagome Lattice Based Chiral Higher-Order Topological Insulator

TL;DR

This paper investigates the topological corner states in a Kagome lattice-based higher-order topological insulator, revealing shape-dependent gapless or gapped corners and proposing a general scheme for classifying such states using Wilson loop formalism.

Contribution

It introduces a new model on the breathing Kagome lattice and a pumping cylinder method to analyze and classify corner states in HOTIs, extending understanding beyond square lattice models.

Findings

Corner states can be conditionally gapless or always gapped depending on lattice shape.

Eigenvalues of Wannier Hamiltonian cross a reference point during pumping, indicating topological corner states.

The method can be generalized to classify corner and hinge states in HOTIs.

Abstract

The higher-order topological insulator (HOTI) protected by spacial symmetry has been studied in-depth on models with square lattice. Our work, based on an alternative model on the breathing Kagome lattice, revealed that the different types of corners in the lattice could actually be conditionally gapless, or always gapped. Using the Wilson loop formalism, we argue that these corner states occur when the eigenvalues of the Wannier Hamiltonian cross through a certain reference point during the conceptual "pumping" procedure. The results demonstrate the corner of the Kagome lattice based HOTI is a zero-dimensional analogue of the 1D chiral edge states on the boundary of a Chern insulator, but with a sensitive dependence on the shape of the corner. Our method of the pumping cylinder, which reveals the symmetry/gapless-ability correspondence, can be generalized into a general scheme in determining the classification of corner(hinge) states in HOTI.