Higher-order band topology

By Biye Xie, Hai-Xiao Wang, Xiujuan Zhang, P. Zhan, Jian‐Hua Jiang, Minghui Lu, Yan-Feng Chen. Nature Reviews Physics, 2020

468 citations recorded by the source corpus.

A conventional topological insulator (TI) has gapped bulk states but gapless edge states. The emergence of the gapless edge states is dictated by the bulk topological invariant of the insulator and the preservation of relevant symmetries. Over the past four years, a new type of TI has been found, which hosts gapless hinge or corner states, rather than edge states. These unconventional TIs, termed higher-order TIs (HOTIs), are common among crystalline and quasi-crystalline materials. Higher-order band topology expands our previous understanding of topological phases and provides unprecedented lower-dimensional boundary states for devices. Here, we review the principles, theories and experimental realizations of HOTIs for both electrons and classical waves. There is an emphasis on the development of HOTIs in photonic, phononic and circuit systems owing to their special contributions to these fields. From these discussions, we remark on trends and challenges in the field and the impact of higher-order band topology on other scientific disciplines. The recent discovery of higher-order band topology in topological insulators has unveiled the hierarchical structure of topological band theory. This Perspective reviews this rapidly developing field and discusses future directions, including open challenges, future trends, synergy and its use in other fields and potential applications.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/4951a88d92a18db7880b72871cfc5176a9d1d998

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. M. Xiao
2. Tao Liu
3. Meng Kang
4. C. T. Chan
5. Tian Zhang
6. Xiujuan Zhang
7. Yan-Feng Chen
8. Ming-Hui Lu

In Materials Chemistry

1. C. T. Chan
2. M. Xiao
3. Xiujuan Zhang
4. Yan-Feng Chen
5. Ming-Hui Lu

Citations in the corpus

• A review on non-Hermitian skin effect (2022, background): “14 especially in classical wave systems where artificial materials provide highly controllable and designable platforms for the realization of novel topological phases that are elusive or even absent in naturally-occurring materials [133, 134, 146-148].”
• Applications of bound states in the continuum in photonics (2023, background): “These topological phases exhibit a higher-order bulk–boundary correspondence such that a D -dimensional non-trivial bulk guarantees ( D d − )-dimensional ( ⋯ d D = 2,3, , ) boundary modes such as corner or hinge states 226 .”
• Tailoring Structure‐Borne Sound through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review (2022, unknown): “phenomenon often requires a higher-order topology [297].”