Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence

Abstract

Topological phases characterized by non-Abelian charges are beyond the scope of the paradigmatic tenfold way and have gained increasing attention recently. Here we investigate topological insulators with multiple tangled gaps in Floquet settings and identify uncharted Floquet non-Abelian topological insulators without any static or Abelian analog. We demonstrate that the bulk-edge correspondence is multifold and follows the multiplication rule of the quaternion group $Q_8$. The same quaternion charge corresponds to several distinct edge-state configurations that are fully determined by phase-band singularities of the time evolution. In the anomalous non-Abelian phase, edge states appear in all bandgaps despite trivial quaternion charge. Furthermore, we uncover an exotic swap effect -- the emergence of interface modes with swapped driving, which is a signature of the non-Abelian dynamics and absent in Floquet Abelian systems. Our work, for the first time, presents Floquet topological insulators characterized by non-Abelian charges and opens up exciting possibilities for exploring the rich and uncharted territory of non-equilibrium topological phases.

8+7 pages

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• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Floquet non-Abelian topological charges and edge states
• Hybrid-Order Topological Phase And Transition in 1H Transition Metal Compounds
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Analytic bulk-edge connection in circular-symmetric models
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators
• Non-Abelian interference of topological edge states
• Coupled-wire construction of non-Abelian higher-order topological phases
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems