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 zero MCMs, no MCMs, only anomalous $\pi$ MCMs, and both regular zero and anomalous $\pi$ MCMs. To circumvent the subtle issue of characterizing zero and $\pi$ 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. Our study paves the way for the realization of dynamical quadrupolar and octupolar topological superconductors.

• Received 26 January 2022
• Revised 21 March 2022
• Accepted 29 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.155406