Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topolog...Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.展开更多
基金supported by the National Natural Science Foundation of China(52071218)Shenzhen Science and Technology Innovation Commission(20200731215211001 and 20200814110413001)Guangdong Basic and Applied Basic Research Foundation(2022A1515012492)。
基金This work was financially supported by the National Natural Science Foundation of China(22025108 and 21905188)the major project of Basic Science(Natural Science)of Jiangsu Province(21KJA430001)+3 种基金Jiangsu Provincial Natural Science Foundation(BK20211316)Suzhou Municipal Science and Technology Bureau(SYG202125)the State Key Laboratory of Physical Chemistry of Solid Surfaces,Xiamen University(202113)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)and Collaborative Innovation Center of Suzhou Nano Science and Technology。
基金the Singapore Ministry of Education Academic Research Fund Tier-3 Grant No.MOE2017T3-1-001(WBS.No.R-144-000-425-592)the Singapore National Research Foundation Grant No.NRF-NRFI2017-04(WBS No.R-144-000-378-281)。
文摘Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.
