  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.
