Multiple Bulk-Boundary Correspondences and Anomalous Modes in a Non-Hermitian Creutz Ladder

Abstract

The synergy of non-Hermitian and topology renders the bulk-boundary correspondence (BBC) even more elusive. Here we study a non-Hermitian Creutz ladder that incorporates both gain-loss and nonreciprocity, and construct multiple BBCs involving scale-free, normal and anomalous skin modes, as well as topological zero-energy modes. In the presence of spatial inversion (P) symmetry, the parity-time (PT) phase transition is characterized by an average winding number,whereas a hidden chiral symmetry guarantees that topological phase transitions can be detected via a Z 2 invariant. The gain-loss breaks the P symmetry but preserves the combined PT symmetry, and then the previous BBC version only requires minor modifications. Intriguingly, sublattice symmetry enables the precise calculation of non-Bloch spectra, based on which a hybrid spectral winding can encode the localization (or delocalization) information of two counterintuitive bulk modes that coexist with normal skin modes. One type exhibits exponential boundary accumulation in the opposite direction to nonreciprocity. The other exemplifies a surge of Bloch-wave states in nonreciprocal lattices. These results reveal a series of unexpected phenomena governed by symmetry, thereby expanding our fundamental understanding of the BBC mechanism in non-Hermitian topological systems.