Dynamical construction of higher-order topological systems

We propose a three-step periodic drive protocol to engineer two-dimensional (2D) Floquet quadrupole superconductors and three-dimensional (3D) Floquet octupole superconductors hosting zero-dimensional Majorana corner modes (MCMs), based on unconventional d-wave superconductivity. Remarkably, the driven system conceives four phases with only 0 MCMs, no MCMs, only anomalous π MCMs, and both regular 0 and anomalous π MCMs. To circumvent the subtle issue of characterizing 0 and π MCMs separately, we employ the periodized evolution operator to architect the dynamical invariants, namely quadrupole and octupole motion in 2D and 3D, respectively, that can distinguish different higher-order topological phases unambiguously. Furthermore, we extend our study using the periodic harmonic drive and generalize the definitions of the dynamical quadrupolar moment for this drive.