Floquet generation of a second-order topological superconductor

We theoretically investigate the Floquet generation of a second-order topological superconducting (SOTSC) phase hosting Majorana corner modes (MCMs), considering a quantum spin Hall insulator with a proximity-induced superconducting $s$-wave pairing in it. Our dynamical prescription consists of the periodic kick in time-reversal symmetry breaking the in-plane magnetic field and fourfold rotational symmetry breaking the mass term in the bulk while these Floquet MCMs are preserved by antiunitary particle-hole symmetry. The first driving protocol always leads to four zero-energy MCMs (i.e., one Majorana state per corner) as a sign of a strong SOTSC phase. Interestingly, the second protocol can result in a weak SOTSC phase, harboring eight zero-energy MCMs (two Majorana states per corner), in addition to the strong SOTSC phase. We characterize the topological nature of these phases by a Floquet quadrupolar moment and Floquet Wannier spectrum. We believe that relying on the recent experimental advancement in the driven systems and proximity - superconductivity, our schemes may be possible to test in the future.