The spin-dependent propagation of electrons in helical nanowires is investigated. We show that the interplay of spin angular momentum and nanowire chirality, under spin-orbit interaction, lifts the symmetry between left and right propagating electrons, giving rise to a velocity asymmetry. The study is based on a microscopic tight-binding model that takes into account the spin-orbit interaction. The continuity equation for the spin-dependent probability density is derived, including the spin non-conserving terms, and quantum dynamics calculations are performed to obtain the electron propagating dynamics. The calculations are applied to the inorganic double-helix SnIP, a quasi-1D material that constitutes a semiconductor with a band gap of ~ 1.9 eV. The results, nevertheless, have general validity due to symmetry considerations. The relation of the propagation velocity asymmetry with the phenomena ascribed to the chiral-induced spin selectivity (CISS) effect is examined.
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