Higher-order topological solitonic insulators

Zhixiong Li,Xiangrong Wang,Yunshan Cao,Peng Yan

doi:10.1038/s41524-019-0246-4

Abstract

Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we theoretically study the dipolar-coupled gyration motion of magnetic solitons on the two-dimensional breathing kagome lattice. We calculate the phase diagram and predict both the Tamm–Shockley edge modes and the second-order corner states when the ratio between alternate lattice constants is greater than a critical value. We show that the emerging corner states are topologically robust against both structure defects and moderate disorders. Micromagnetic simulations are implemented to verify the theoretical predictions with an excellent agreement. Our results pave the way for investigating higher-order topological insulators based on magnetic solitons.

Highlights

A higher-order, e.g., kth-order, topological insulator allows ðn À kÞ-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index.[5,6,7,8,9,10,11,12]
We have investigated the higher-order topological insulator in triangle-shaped and parallelogram-shaped breathing kagome lattice of magnetic vortices
It was found that the second-order topological corner state emerge only under a nance on the breathing kagome and pyrochlore lattices

Summary

Introduction

Topological insulators are receiving considerable attention owing to their peculiar properties, such as chiral edge states, and potential applications in spintronics and quantum computing.[1,2,3,4] A conventional n-dimensional topological insulator only has ðn À 1Þ-dimensional (first-order) topological edge/surface modes according to the bulk-boundary correspondence.[1,2] a higher-order, e.g., kth-order, topological insulator allows ðn À kÞ-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index.[5,6,7,8,9,10,11,12] Interestingly, the experimental evidences of higher-order topological insulators (HOTIs) were reported so far only in classical mechanical and electromagnetic metamaterials.[13,14,15,16,17,18,19,20,21] In terms of applications of HOTIs in spintronics, it is intriguing to ask if they can exist in magnetic system which is intrinsically, nonlinear, in contrast to its phononic and photonic counterparts.Spin waves (or magnons) and magnetic solitons are two important excitations in magnetic system. Topological insulators are receiving considerable attention owing to their peculiar properties, such as chiral edge states, and potential applications in spintronics and quantum computing.[1,2,3,4] A conventional n-dimensional topological insulator only has ðn À 1Þ-dimensional (first-order) topological edge/surface modes according to the bulk-boundary correspondence.[1,2] a higher-order, e.g., kth-order, topological insulator allows ðn À kÞ-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index.[5,6,7,8,9,10,11,12] Interestingly, the experimental evidences of higher-order topological insulators (HOTIs) were reported so far only in classical mechanical and electromagnetic metamaterials.[13,14,15,16,17,18,19,20,21] In terms of applications of HOTIs in spintronics, it is intriguing to ask if they can exist in magnetic system which is intrinsically, nonlinear, in contrast to its phononic and photonic counterparts. Topological chiral edge states are discovered in a two-dimensional honeycomb lattice of magnetic solitons.[48,49] all these topological magnonic and solitonic states are first-order in nature, according to the classification of topological insulators mentioned above

Methods

Results

Conclusion