Floquet Hopf Insulators

Abstract

We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf $\mathbb{Z}$ invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet ${\mathbb{Z}}_2$ 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 quasienergy 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 $\pi$-quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.

6 + 9 pages, 3 + 1 figures

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Cited by in corpus (27)

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• Collisions of ultracold molecules in bright and dark optical dipole traps
• Bimorphic Floquet Topological Insulators
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Realizing Hopf Insulators in Dipolar Spin Systems
• Floquet higher-order Weyl and nexus semimetals
• Non-Abelian Hopf-Euler insulators
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• Multiplicative topological phases
• Floquet and Anomalous Floquet Weyl Semimetals
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• Digital Quantum Simulation of Floquet Topological Phases with a Solid-State Quantum Simulator
• Correlated Hopf insulators