So we realize a second-order topological insulator in the quasienergy-0 gap, and a Weyl semimetal in the quasienergy- π / T gap. Due to the topological charge of the Weyl point, Weyl semimetals can be sliced into a family of two-dimensional (2D) Chern and normal insulators parametrized by k z. The existence of Weyl points indicates the formation of a Weyl semimetal phase at the π / T gap. With the introduction of perturbation, two three-dimensional bands with a linear dispersion are degenerate at two isolated momentum points, which are called Weyl points. So we believe that there is a higher-order topological phase at this gap. According to topological classification, the higher-order topological number can be defined. As shown in (a), the band gap labeled in cyan color indicates that there are gapless chiral hinge states in this gap. Schematic of (a) an anomalous Floquet higher-order topological insulator and (b) a composite topological phase.
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