Waveguiding in two-dimensional Floquet non-Abelian topological insulators

Topological phases characterized by non-Abelian charges have garnered increasing attention recently. Although Floquet (periodic-driving) higher-order topological phases have been explored at the single-particle level, the role of interactions in non-Abelian topological insulators with multiple entangled energy gaps remains incompletely understood. In this work, we extend previous research by investigating higher-order topological phases featuring non-Abelian charges through Floquet engineering. Here we construct a model for two-dimensional non-Abelian higher-order topological phases on a square lattice subjected to two-step periodic driving. We find that the corner and edge states emerge and appear in all energy gaps despite the quaternion charge being trivial. Moreover, spatially exchanging the driving generates exotic interface modes-a hallmark of non-Abelian dynamics, namely non-commutativity. Notably, the non-zero composite Chern number demonstrates the non-triviality of the Floquet non-Abelian system with. We further reveal that the configuration of these quaternion-charge edge states is entirely determined by the quadruple degenerate phase-band singularities in the time evolution. Our work provides a platform for studying higher-order topological states and non-equilibrium quantum dynamics.