Hybrid higher-order skin-topological modes in non-reciprocal systems

Higher-order phases are characterized by corner or hinge modes that arise due to the interesting interplay of localization mechanisms along two or more dimensions. In this work, we introduce and construct a novel class of "hybrid" higher-order skin-topological boundary modes in non-reciprocal systems with two or more open boundaries. Their existence crucially relies on non-reciprocal pumping in addition to topological localization. Unlike usual non-Hermitian "skin" modes, they can exist in lattices with \emph{vanishing} net reciprocity due to the selective nature of non-reciprocal pumping: While the bulk modes remain extended due to the cancellation of non-reciprocity within each unit cell, boundary modes experience a curious \emph{spontaneous breaking} of reciprocity in the presence of topological localization, thereby experiencing the non-Hermitian skin effect. The number of possible hybridization channels increases rapidly with dimensionality, leading to a proliferation of distinct phases. In addition, skin modes or hybrid skin-topological modes can restore unitarity and are hence stable, allowing for experimental observations and manipulations in non-Hermitian photonic and electrical metamaterials.