Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice

We study theoretically the interplay effect of Zeeman field and modulated spin-orbit coupling on topological properties of a one-dimensional dimerized lattice, known as Su-Schrieffer-Heeger model. We find that in the weak (strong) modulated spin-orbit coupling regime, trivial regions or nontrivial ones with two pairs of zero-energy states can be turned into nontrivial regions by applying a uniform (staggered) perpendicular Zeeman field through a topological phase transition. Furthermore, the resulting nontrivial phase hosting a pair of zero-energy boundary states can survive within a certain range of the perpendicular Zeeman field magnitude. Due to the effective time-reversal, particle-hole, chiral, and inversion symmetries, in the presence of either uniform or staggered perpendicular Zeeman field, the topological class of the system is BDI which can be characterized by $\mathbbm{Z}$ index. We also examine the robustness of the nontrivial phase by breaking the underlying symmetries giving rise that inversion symmetry plays an important role.