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  • Letter
  • Open Access

Unified characterization for higher-order topological phase transitions

Wei Jia1,2, Xin-Chi Zhou1,2, Lin Zhang3, Long Zhang4, and Xiong-Jun Liu1,2,5,*

  • 1International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
  • 2Hefei National Laboratory, Hefei 230088, China
  • 3ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
  • 4School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
  • 5International Quantum Academy, Shenzhen 518048, China

  • *xiongjunliu@pku.edu.cn
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Phys. Rev. Research 5, L022032 – Published 15 May, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022032

Abstract

Higher-order topological phase transitions (HOTPTs) are associated with closing either the bulk energy gap (type-I) or boundary energy gap (type-II) without changing symmetry, and conventionally, both transitions are captured in real space and characterized separately. Here, we propose a momentum-space topological characterization of HOTPTs which unifies both types of topological transitions and enables a precise detection by quench dynamics. Our unified characterization is based on a correspondence between mass domain walls on real-space boundaries and higher-order band-inversion surfaces (BISs) which are characteristic interfaces in the momentum subspace. Topological transitions occur when momentum-space topological nodes, dubbed higher-order topological charges, cross the higher-order BISs after proper projection. Particularly, the bulk (boundary) gap closes when all (part of) topological charges cross the BISs, characterizing type-I (type-II) HOTPTs. These distinct dynamical behaviors of higher-order topological charges can be feasibly measured from quench dynamics driven with control in experiments. Our work opens an avenue to characterize and detect the two types of HOTPTs within a unified framework and shall advance research in both theory and experiments.

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Phys. Rev. Research 5, L022032– Published 15 May, 2023
  • Received 26 September 2022
  • Accepted 13 April 2023
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