Floquet Hopf Insulators

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

Research output: Contribution to journalArticlepeer-review

25 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

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© 2019 American Physical Society.


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