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

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.