Hopf characterization of two-dimensional Floquet topological insulators

Ünal, F. Nur; Eckardt, André; Slager, Robert-Jan

doi:10.1103/physrevresearch.1.022003

Title: Hopf characterization of two-dimensional Floquet topological insulators

Journal Article · 09 September 2019 · Physical Review Research

DOI: https://doi.org/10.1103/physrevresearch.1.022003 · OSTI ID:1560766

^[1]; Eckardt, André ^[1]; Slager, Robert-Jan ^[2]

Max Planck Inst. fuer Physik komplexer Systeme, Dresden (Germany)
Harvard Univ., Cambridge, MA (United States)

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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Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for the Advancement of Topological Semimetals (CATS); Ames Laboratory (AMES), Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); German Research Foundation (DFG)

Grant/Contract Number:: AC02-07CH11358; 277974659

OSTI ID:: 1560766

Alternate ID(s):: OSTI ID: 1767792

Journal Information:: Physical Review Research, Vol. 1, Issue 2; ISSN 2643-1564

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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