Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics

This article introduces a general and experimentally feasible protocol to engineer dynamic higher-order topological phases by periodically driving its static lower-order counterparts with a suitable discrete symmetry breaking Dirac mass perturbation. Realization of dynamic corner modes in 2D, protected by a quantized Floquet quadrupole moment, exemplifies this general protocol. Additionally, the authors show that corner modes leave their signature even in a quantum spin Hall insulator for a long time after a sudden quench, manifesting their topological nature through periodic appearances of partial and complete revival of the survival probability.