Floquet Hopf Insulators

• Published in: Physical review letters Vol. 123; no. 26; p. 266803
• Main Authors: Schuster, Thomas, Gazit, Snir, Moore, Joel E, Yao, Norman Y
• Format: Journal Article
• Language: English
• Published: United States 31.12.2019
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.123.266803

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 Z_{2} 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.