Generation and time evolution of anomalous Floquet Majorana flat edge modes in two-dimensional noncolinear magnet-superconductor heterostructures

Abstract

We theoretically investigate the realization of gapless Floquet topological superconducting phases in a two-dimensional magnet-superconductor heterostructure (2D Shiba lattice) in the presence of a harmonic drive implemented in the chemical potential. Employing a real-space tight-binding model, we obtain both the regular $0$- and anomalous $π$-Floquet Majorana flat edge modes (FMFEMs) in the quasi-energy spectrum. We also study the real-time evolution of the FMFEMs and analyze their local density of states in the presence of such a periodic drive. The topological characterization is performed using the winding number, exploiting the chiral symmetry of the equivalent bulk effective momentum-space Hamiltonian. This is also supported by the corresponding edge state spectra. Furthermore, we employ the Brillouin-Wigner (BW) and Floquet perturbation theory (FPT) to gain analytical insight into the problem. We compare our exact (numerical), BW, and FPT results in terms of the quasi-energy spectra obtained across different frequency regimes. We find good agreement between the exact numerical, BW, and FPT results in the higher-frequency and high-amplitude domain, particularly close to the $0$-quasi-energy modes.