Dynamical construction of Quadrupolar and Octupolar topological superconductors

TL;DR

This paper introduces a three-step periodic drive protocol to engineer higher-order Floquet topological superconductors with Majorana corner modes, using unconventional $d$-wave pairing to realize distinct dynamical topological phases.

Contribution

It presents a novel method to dynamically create 2D and 3D Floquet quadrupole and octupole topological superconductors with Majorana modes, employing dynamical invariants for phase characterization.

Findings

Four distinct Floquet topological phases identified.

Dynamical invariants effectively distinguish topological phases.

Protocol enables realization of higher-order topological superconductors.

Abstract

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 $\pi$ MCMs, and both regular $0$ and anomalous $\pi$ MCMs. To circumvent the subtle issue of characterizing $0$ 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.