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Title: Hopf characterization of two-dimensional Floquet topological insulators

Abstract

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.

Authors:
ORCiD logo; ;
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for the Advancement of Topological Semimetals (CATS); Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); German Research Foundation (DFG)
OSTI Identifier:
1560766
Alternate Identifier(s):
OSTI ID: 1767792
Grant/Contract Number:  
AC02-07CH11358; 277974659
Resource Type:
Published Article
Journal Name:
Physical Review Research
Additional Journal Information:
Journal Name: Physical Review Research Journal Volume: 1 Journal Issue: 2; Journal ID: ISSN 2643-1564
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; optics; charge transport; magnetism and spin physics; materials and chemistry by design; synthesis (novel materials); synthesis (predictive)

Citation Formats

Ünal, F. Nur, Eckardt, André, and Slager, Robert-Jan. Hopf characterization of two-dimensional Floquet topological insulators. United States: N. p., 2019. Web. https://doi.org/10.1103/PhysRevResearch.1.022003.
Ünal, F. Nur, Eckardt, André, & Slager, Robert-Jan. Hopf characterization of two-dimensional Floquet topological insulators. United States. https://doi.org/10.1103/PhysRevResearch.1.022003
Ünal, F. Nur, Eckardt, André, and Slager, Robert-Jan. Mon . "Hopf characterization of two-dimensional Floquet topological insulators". United States. https://doi.org/10.1103/PhysRevResearch.1.022003.
@article{osti_1560766,
title = {Hopf characterization of two-dimensional Floquet topological insulators},
author = {Ünal, F. Nur and Eckardt, André and Slager, Robert-Jan},
abstractNote = {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.},
doi = {10.1103/PhysRevResearch.1.022003},
journal = {Physical Review Research},
number = 2,
volume = 1,
place = {United States},
year = {2019},
month = {9}
}

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