Unified characterization of the complete hierarchy of topological boundary states in a Floquet crystalOA
Topological phases of matter are defined by bulk invariants that dictate the existence of robust boundary states.While conventional bulk-boundary correspondence links a given bulk invariant to a specific type of boundary mode,many systems may host multiple orders of topology simultaneously,including chiral edge states,weak edge states,and higher-order hinge and corner states.A unified framework for predicting and classifying all such boundary phenomena has remained elusive.Here,we introduce a compact topological triplet—three complementary one-dimensional winding numbers defined in distinct momentum subspaces—that fully determines the presence and type of boundary states in two-dimensional Floquet crystals.We experimentally implement this concept in a time-synthetic photonic lattice,demonstrating its predictive power.This unified approach integrates strong,weak,and higher-order topology into a single framework,providing critical insight for studying topological matter and enabling systematic control of complex topological phases across a broad range of physical platforms.
Yuxiang Guo;Zhoutao Lei;Jizhou Wu;Jiankun Zhu;Yao Qin;Linhu Li;Jingyun Fan
State Key Laboratory of Quantum Functional Materials and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China Shenzhen Institute for Quantum Science and Engineering and Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,ChinaGuangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy,Sun Yat-Sen University(Zhuhai Campus),Zhuhai 519082,ChinaState Key Laboratory of Quantum Functional Materials and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area(Guangdong),Shenzhen 518045,ChinaShenzhen Institute for Quantum Science and Engineering and Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,ChinaState Key Laboratory of Quantum Functional Materials and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,ChinaGuangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy,Sun Yat-Sen University(Zhuhai Campus),Zhuhai 519082,China Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area(Guangdong),Shenzhen 518045,ChinaState Key Laboratory of Quantum Functional Materials and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China Shenzhen Institute for Quantum Science and Engineering and Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China Center for Advanced Light Source,Southern University of Science and Technology,Shenzhen 518055,China Hefei National Laboratory,Hefei 230088,China
数理科学
topological phaseFloquet systemsynthetic latticedomain wall
《National Science Review》 2026 (12)
P.30-39,10
supported by the Key-Area Research and Development Program of Guangdong Province(2020B0303010001,2019ZT08X324 and 2019CX01X042)the Innovation Program for Quantum Science and Tech-nology(2021ZD0300804)the National Natural Science Foundation of China(12474159).
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