Floquet engineering of point-gapped topological superconductors

Non-Hermitian systems exhibit two distinct topological classifications based on their gap structure: line-gap and point-gap topologies. Although point-gap topology is intrinsic to non-Hermitian systems, the systematic construction of the point-gapped topological phases remains challenging. Here, we present the Floquet engineering approach for realizing point-gapped topological superconductors. By combining Floquet theory with particle-hole symmetry, we show that a point gap hosting robust Majorana edge modes emerges at the overlap of Floquet bands with opposite winding numbers. In the thermodynamic limit, even weak non-Hermiticity opens a point gap from a gapless spectrum, driving a topological phase transition and breaking non-Bloch parity-time ($\mathcal{PT}$) symmetry. This transition is accompanied by the appearance of the Floquet ${Z}_{2}$ skin effect. Furthermore, the point-gapped topological phase and the non-Bloch $\mathcal{PT}$ symmetry exhibit size-dependent phenomena driven by the critical skin effect. Our work offers a pathway for exploring the point-gapped topological phases in non-Hermitian systems.