Takagi Topological Insulator on the Honeycomb Lattice

TL;DR

This paper reviews a novel second-order topological insulator on the honeycomb lattice, characterized by a $PT$-symmetry-protected topological invariant related to the Stiefel-Whitney number and Takagi's factorization, featuring corner zero modes.

Contribution

It introduces a simple model demonstrating a second-order topological insulator with $PT$ symmetry on the honeycomb lattice, connecting topological invariants to physical edge states.

Findings

Identification of a second-order topological insulator with corner zero modes

Connection of the Stiefel-Whitney number to Takagi's factorization under sublattice symmetry

Demonstration of the model's topological properties on the honeycomb lattice

Abstract

Recently, real topological phases protected by $PT$ symmetry have been actively investigated. In two dimensions, the corresponding topological invariant is the Stiefel-Whitney number. A recent theoretical advance is that in the presence of the sublattice symmetry, the Stiefel-Whitney number can be equivalently formulated in terms of Takagi's factorization. The topological invariant gives rise to a novel second-order topological insulator with odd $PT$-related pairs of corner zero modes. In this article, we review the elements of this novel second-order topological insulator, and demonstrate the essential physics by a simple model on the honeycomb lattice.