Hopf characterization of two-dimensional Floquet topological insulators
View / Open Files
Authors
Ünal, FN
Eckardt, A
Slager, RJ
Publication Date
2019Journal Title
Physical Review Research
ISSN
2643-1564
Publisher
American Physical Society (APS)
Volume
1
Issue
2
Number
022003
Pages
022003
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Ünal, F., Eckardt, A., & Slager, R. (2019). Hopf characterization of two-dimensional Floquet topological insulators. Physical Review Research, 1 (2. 022003), 022003. https://doi.org/10.1103/PhysRevResearch.1.022003
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.
Keywords
cond-mat.quant-gas, cond-mat.quant-gas, cond-mat.mes-hall, physics.atom-ph, quant-ph
Identifiers
External DOI: https://doi.org/10.1103/PhysRevResearch.1.022003
This record's URL: https://www.repository.cam.ac.uk/handle/1810/336113
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.