Non-Hermitian extended midgap states and bound states in the continuum

Abstract

We investigate anomalous localization phenomena in non-Hermitian systems by solving a class of generalized Su-Schrieffer-Heeger/Rice-Mele models and by relating their provenance to fundamental notions of topology, symmetry-breaking, and biorthogonality. We find two types of bound states in the continuum, both stable even in the absence of chiral symmetry: the first being skin bulk states, which are protected by the spectral winding number. The second type is constituted by boundary modes associated with a quantized biorthogonal polarization. Furthermore, we find an extended state stemming from the boundary state that delocalizes while remaining in the gap at bulk critical points. This state may also delocalize within a continuum of localized (skin) states. These results clarify fundamental aspects of topology and symmetry in light of different approaches to the anomalous non-Hermitian bulk-boundary correspondence and are of direct experimental relevance for mechanical, electrical, and photonic systems.