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.
- Received 26 September 2022
- Accepted 13 April 2023
DOI:https://doi.org/10.1103/PhysRevResearch.5.L022032
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society