期刊
PHYSICAL REVIEW RESEARCH
卷 1, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevResearch.1.022003
关键词
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资金
- Deutsche Forschungsgemeinschaft (DFG) [FOR 2414, 277974659]
- Center for the Advancement of Topological Materials initiative, an Energy Frontier Research Center - US Department of Energy, Office of Science
We present a topological characterization of time-periodically driven two-band models in 2 + 1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three-dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.
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