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Topological states in chiral electronic chains

We consider the influence of topological phases, or their vicinity, on the spin density and spin polarization through a chiral chain. We show the quantization of the Berry phase in a one-dimensional polarization helix structure, under the presence of an external magnetic field, and show its influence on the spin density. The polar angle of the momentum space spin density becomes quantized in the regime that the Berry phase is quantized, as a result of the combined effect of the induced spin-orbit coupling and the external transverse magnetic field, while the edge states do not show the polar angle quantization, in contrast with the bulk states. Under appropriate conditions, the model can be generalized to have similarities with a chain with nonhomogeneous Rashba spin- orbit couplings, with zero- or low-energy edge states. Due to the breaking of time-reversal symmetry, we recover the effect of chiral-induced spin polarization and spin transport across the chiral chain, when coupling to external leads. Some consequences of the quantized spin polarization and low-energy states on the spin transport are discussed.