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.
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.
The complete characterization of a generic
d-dimensional Floquet topological phase is usually hard for the requirement of information about the micromotion throughout the entire driving period. In a recent work [L. Zhang et al., Phys. Rev. Lett. 125, 183001 (2020)], an experimentally feasible dynamical detection scheme was proposed to characterize the integer Floquet topological phases using quantum quenches. However, this theory is still far away from completion, especially for free-fermion Floquet topological phases, where the states can also be characterized by
Z2 invariants. Here we develop a full and unified dynamical characterization theory for the
Z2 Floquet topological phases of different dimensionality and tenfold-way symmetry classes by quenching the system from a trivial and static initial state to the Floquet topological regime through suddenly changing the parameters and turning on the periodic driving. By measuring the minimal information of Floquet bands via the stroboscopic time-averaged spin polarizations, we show that the topological spin texture patterns emerging on certain discrete momenta of Brillouin zone called the 0 or $\ensuremath{\pi}$ gap highest-order band-inversion surfaces provide a measurable dynamical
Z2 Floquet invariant, which uniquely determines the Floquet boundary modes in the corresponding quasienergy gap and characterizes the
Z2 Floquet topology. The applications of our theory are illustrated via one- and two-dimensional models that are accessible in current quantum simulation experiments. Our work provides a highly feasible way to detect the
Z2 Floquet topology and completes the dynamical characterization for the full tenfold classes of Floquet topological phases, which shall advance the research in theory and experiments.