Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations

TL;DR

This paper explores how magnetic edge configurations in zigzag graphene nanoflakes induce second-order topological states, revealing robust corner states that are unaffected by defects or disorder, and highlighting the role of magnetic orientation.

Contribution

It demonstrates the realization of high-order topological states in graphene nanoflakes through magnetic edge states, even with zero net magnetization.

Findings

Edge ferromagnetism or antiferromagnetism breaks time-reversal symmetry.

Topological in-gap corner states emerge due to a second-order phase transition.

Corner states are robust against defects and magnetic disorder.

Abstract

We study the energy spectrum and energy levels of the extended Kane-Mele model with magnetic atoms on their zigzag edges. It is demonstrated that the edges of ferromagnetism or antiferromagnetism are enough to break the time-reversal symmetry and host one-dimensional gapped edge states. Thus, a second-order topological phase transition could happen, which leads to the emergence of topological in-gap zero-dimensional corner states. We also prove that the in-gap corner states are robust against corner defects and magnetic disorder. Our proposal based on the edge antiferromagnetism shows that the high-order topological states can be realized, although the net magnetization of the material is zero. In addition, we discuss the influence of spin magnetization orientation on the degeneracy and energy of in-gap corner states.