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

TL;DR

This paper theoretically explores how Zeeman fields and modulated spin-orbit coupling induce and control topological phases in a one-dimensional dimerized lattice, revealing conditions for the emergence and robustness of zero-energy boundary states.

Contribution

It demonstrates how Zeeman fields can induce topological phase transitions in a dimerized lattice with modulated spin-orbit coupling, expanding understanding of topological phase control.

Findings

Zeeman fields can turn trivial regions into nontrivial topological phases.

Nontrivial phases with zero-energy boundary states can persist over certain Zeeman field ranges.

Symmetry analysis shows the system belongs to class BDI with a $$ index.

Abstract

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.