Time evolution of Majorana corner modes in Floquet second-order topological superconductor

TL;DR

This paper introduces a feasible sinusoidal drive protocol to generate and analyze Floquet second-order topological superconductors with Majorana corner modes, combining numerical and analytical methods.

Contribution

It presents a novel drive protocol to realize Floquet second-order topological superconductors with Majorana corner modes and compares numerical and Floquet perturbation theory results.

Findings

Successful generation of 2D Floquet second-order topological superconductor

Identification of both 0- and π-Majorana corner modes

Good agreement between numerical and analytical results at high frequencies

Abstract

We propose a practically feasible time-periodic sinusoidal drive protocol in onsite mass term to generate the two-dimensional~(2D) Floquet second-order topological superconductor, hosting both the regular $0$- and anomalous $\pi$-Majorana corner modes~(MCMs) while starting from a static 2D topological insulator/$d$-wave superconductor heterostructure setup. We theoretically study the local density spectra and the time dynamics of MCMs in the presence of such drive. The dynamical MCMs are topologically characterized by employing the average quadrupolar motion. Furthermore, we employ the Floquet perturbation theory~(FPT) in the strong driving amplitude limit to provide analytical insight into the problem. We compare our exact (numerical), and the FPT results in terms of the eigenvalue spectra and the time dynamics of the MCMs. We emphasize that the agreement between the exact numerical and the FPT results are more prominent in the higher frequency regime for close to the $0$-quasi-energy mode.