We investigate an extended spin-full Su-Schrieffer-Heeger (SSH) model preserving chiral symmetry. It contains spin-mixing and nonmixing Rashba spin-orbit interactions, complex next to next nearest neighbor (NNNN) hopping. Using the theory of non-Hermitian matrices, we construct a Hamiltonian function facilitating exact analysis of the system. When the two types of Rashba interactions are present, the spectrum changes from band crossing to band touching having Dirac cone. The gap-closing condition for the spectrum and its symmetry is derived in detail. The phase diagram shows rich topological phases with winding number 1 or 2, re-entrant phase transitions, and multicritical points. An extension of the model to $\mathcal{M}$ coupled chains exhibits topological phases with winding number varying from one to $2\mathcal{M}$, and it is further characterized by the Zak phase. Remarkably, a domain-wall profile in nearest neighbor hopping can tune the location of mid-gap zero-energy states. The localization properties of the edge modes are characterized by the inverse participation ratio and compared with earlier works. Our model and method could bring a new perspective to certain classes of topological systems.

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• Spin-orbit coupling
• Symmetry protected topological states
• Topological insulators
• Topological materials