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

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 flavours 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 flavour is constituted by boundary modes associated with a quantized biorthogonal polarization. Furthermore, we find the 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 the light of different approaches to the anomalous non-Hermitan bulk-boundary correspondence - and are of direct experimental relevance for mechanical, electrical and photonic systems.