  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.
