Floquet Hopf Insulators

Thomas Schuster, Snir Gazit, Joel E. Moore, Norman Y. Yao

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We predict the existence of a Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf Z invariant, a linking number characterizing the (nondriven) Hopf topological insulator. The second invariant is an intrinsically Floquet Z2 invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time evolution, subject to a process in which defects at different quasienergies exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0 or π quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.

Original languageAmerican English
Article number266803
JournalPhysical Review Letters
Issue number26
StatePublished - 30 Dec 2019

Bibliographical note

Funding Information:
We gratefully acknowledge insightful discussions with M. Bukov and D. Else. This work was supported by the DARPA DRINQS program (Grant No. D18AC00033), the David and Lucile Packard Foundation and the W. M. Keck foundation. T. S. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1752814. S. G. acknowledges support from the Israel Science Foundation, Grant No. 1686/18.

Publisher Copyright:
© 2019 American Physical Society.


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