Skin-effect localization and maximal-order exceptional points in reciprocal Floquet lattices

In systems exhibiting the non-Hermitian skin effect (NHSE), higher-order exceptional points (EPs) exhibit unique characteristics making them invaluable for enhanced lasing and sensing operations. When these critical degeneracies reach a maximal order, equal to the system size N, they induce a collapse of the spectrum, not only into a singular eigenstate but also a singular point in physical space. To date, NHSE EPs of maximal order have been predicted in nonreciprocal systems, such as the Hatano-Nelson lattice, where this collapse occurs in the limit of infinite anisotropy. Challenging this perspective, we demonstrate that reciprocal Floquet systems are capable of exhibiting skin localization of arbitrary strength—ranging from mild localization, to the extreme regime of maximal-order exceptional points. By employing $${{{\mathscr{PT}}}}$$ -symmetry in both space and time, we uncover a unique stroboscopic effect that results in the complete localization of the field amplitude at the edge of the lattice. A phase transition at a critical coupling strength leads to a regime with infinite NHSE EP solutions of maximal-order. Our results are broadly applicable to photonic, acoustic, and electronic systems, allowing one to leverage the dynamics of these valuable degeneracies in entirely new platforms, eliminating the need for critical asymmetric transmission. In non-Hermitian systems, higher-order exceptional points (EPs) and non-Hermitian Skin Effect (NHSE) offer powerful tools for enhanced sensing and lasing. Here, the authors show that reciprocal Floquet lattices with space-time PT-symmetry can host maximal-order NHSE EPs and extreme skin localization without requiring nonreciprocity.