Modeling Spin Transport in Helical Fields: Derivation of an Effective Low-Dimensional Hamiltonian

TLDR

The presented model is general and relevant for spin‑dependent effects in molecular‑scale systems with helical symmetry. The study aims to derive an effective Hamiltonian describing spin transport along a helical pathway with spin‑orbit interaction induced by a helical external field. The authors construct this Hamiltonian in a tight‑binding framework that requires at least two energy levels per site and asymmetries in electronic coupling and spin‑orbit strength to generate net spin polarization. They find that sizable spin polarization can be achieved without phase‑breaking processes when couplings are asymmetric, whereas fully symmetric electronic and spin‑orbit couplings produce no polarization.

Abstract

This study is devoted to a consistent derivation of an effective model Hamiltonian to describe spin transport along a helical pathway and in the presence of spin–orbit interaction, the latter being induced by an external field with helical symmetry. It is found that a sizable spin polarization of an unpolarized incoming state can be obtained without introducing phase breaking processes. For this, at least two energy levels per lattice site in the tight-binding representation are needed. Additionally, asymmetries in the effective electronic-coupling parameters as well as in the spin–orbit interaction strength must be present to achieve net polarization. For a fully symmetric system—in terms of electronic and spin–orbit couplings—no spin polarization is found. The model presented is quite general and is expected to be of interest for the treatment of spin-dependent effects in molecular scale systems with helical symmetry.