Spin Chern phases and persistent spin texture in a quasi 2D SSH model

We construct a quasi-two-dimensional Su Schrieffer-Heeger model (SSH) like model and uncover a rich set of topological phases with nontrivial spin textures in the presence of complex hopping and spin orbit coupling. Despite its simple structure, the combined effect of complex hopping and spin orbit interaction gives rise not only to the conventional quantum anomalous Hall insulating (QAHI) phase, but also to distinct combinations of spin Chern phases, namely quantum anomalous spin Hall insulating (QASHI) phase. Furthermore, we demonstrate that the bulk bands of this model can host persistent spin textures, whose formation and stability are governed by the relative strengths of nearest and next nearest neighbor complex hopping. To elucidate the underlying mechanisms, we develop a low energy continuum theory that captures the emergence of these topological phases and clarifies the origin of the persistent spin textures. Interestingly, the resulting spin textures closely resemble those typically observed in conventional semiconductor systems with topologically trivial band structures. However, in our case, they emerge within a nontrivial topological framework, enabled by carefully engineered hopping patterns that intertwine lattice geometry, complex hopping, and spin orbit coupling