Properties of the non-Hermitian SSH model: role of PT-symmetry

The present work addresses the distinction between the topological properties of PT symmetric and non-PT symmetric scenarios for the non-Hermitian Su-Schrieffer-Heeger (SSH) model. The non-PT symmetric case is represented by non-reciprocity in both the inter- and the intra-cell hopping amplitudes, while the one with PT symmetry is modeled by a complex on-site staggered potential. In particular, we study the loci of the exceptional points, the winding numbers, band structures, and explore the breakdown of bulk-boundary correspondence (BBC). We further study the interplay of the dimerization strengths on the observables for these cases. The non-PT symmetric case denotes a more familiar situation, where the winding number abruptly changes by a half-integer through tuning of the non-reciprocity parameters, and demonstrates a complete breakdown of BBC, thereby showing the non-Hermitian skin effect. The topological nature of the PT symmetric case appears to follow closely to its Hermitian analogue, except that it shows unbroken (broken) regions with complex (purely real) energy spectra, while another variant of the winding number exhibits a continuous behavior as a function of the strength of the potential, while the conventional BBC is preserved.