Wannier representation of Floquet topological states
Abstract
A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled. This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator. In this work, we generalize this characterization of topological phases toward periodically driven systems. We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet topological insulators, anomalous Floquet topological insulators with micromotion-induced boundary states, and gapless Floquet states realized with topological Floquet operators. In particular, nontrivial time dependence of hybrid Wannier centers indicates impossibility of continuous deformation of a driven system into an undriven insulator, and a topological Floquet operator implies an obstruction to constructing a generalized Wannier function which is localized in real and frequency spaces. Our results pave a way to a unified understanding of topological states in periodically driven systems as a topological obstruction in Floquet states.
- Authors:
-
- Univ. of Tokyo (Japan)
- Harvard Univ., Cambridge, MA (United States)
- Max-Planck-Institut für Physik komplexer Systeme, Dresden (Germany); Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden (Germany)
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for the Advancement of Topological Semimetals (CATS); Iowa State Univ., Ames, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Japan Society for the Promotion of Science (JSPS)
- OSTI Identifier:
- 1767741
- Grant/Contract Number:
- AC02-07CH11358; JP16J03619
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; optics, charge transport, magnetism and spin physics, materials and chemistry by design, synthesis (novel materials), synthesis (predictive)
Citation Formats
Nakagawa, Masaya, Slager, Robert-Jan, Higashikawa, Sho, and Oka, Takashi. Wannier representation of Floquet topological states. United States: N. p., 2020.
Web. doi:10.1103/physrevb.101.075108.
Nakagawa, Masaya, Slager, Robert-Jan, Higashikawa, Sho, & Oka, Takashi. Wannier representation of Floquet topological states. United States. https://doi.org/10.1103/physrevb.101.075108
Nakagawa, Masaya, Slager, Robert-Jan, Higashikawa, Sho, and Oka, Takashi. Mon .
"Wannier representation of Floquet topological states". United States. https://doi.org/10.1103/physrevb.101.075108. https://www.osti.gov/servlets/purl/1767741.
@article{osti_1767741,
title = {Wannier representation of Floquet topological states},
author = {Nakagawa, Masaya and Slager, Robert-Jan and Higashikawa, Sho and Oka, Takashi},
abstractNote = {A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled. This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator. In this work, we generalize this characterization of topological phases toward periodically driven systems. We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet topological insulators, anomalous Floquet topological insulators with micromotion-induced boundary states, and gapless Floquet states realized with topological Floquet operators. In particular, nontrivial time dependence of hybrid Wannier centers indicates impossibility of continuous deformation of a driven system into an undriven insulator, and a topological Floquet operator implies an obstruction to constructing a generalized Wannier function which is localized in real and frequency spaces. Our results pave a way to a unified understanding of topological states in periodically driven systems as a topological obstruction in Floquet states.},
doi = {10.1103/physrevb.101.075108},
journal = {Physical Review. B},
number = 7,
volume = 101,
place = {United States},
year = {Mon Feb 10 00:00:00 EST 2020},
month = {Mon Feb 10 00:00:00 EST 2020}
}
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