Floquet engineering of point-gapped topological superconductors

TL;DR

This paper introduces a Floquet engineering method to realize point-gapped topological superconductors with Majorana edge modes in non-Hermitian systems, revealing size-dependent phenomena and a new topological phase transition.

Contribution

It presents a novel Floquet-based approach to systematically construct point-gapped topological superconductors in non-Hermitian systems, incorporating particle-hole symmetry and revealing new size-dependent topological phenomena.

Findings

Weak non-Hermiticity opens a point gap from a gapless spectrum.

Emergence of Floquet $Z_2$ skin effect at the topological transition.

Size-dependent phenomena driven by the critical skin effect.

Abstract

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, its systematic construction remains a challenge. Here, we present the Floquet engineering approach for realizing point-gapped topological superconductors. By combining Floquet theory with particle-hole symmetry (PHS), 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 new pathway for exploring the point-gapped topological phases in non-Hermitian systems.