  The experiment that the high spin selectivity and the length-dependent spin
polarization are observed in double-stranded DNA [Science ${\bf 331}$, 894
(2011)], is elucidated by considering the combination of the spin-orbit
coupling, the environment-induced dephasing, and the helical symmetry. We show
that the spin polarization in double-stranded DNA is significant even in the
case of weak spin-orbit coupling, while no spin polarization appears in
single-stranded DNA. Furthermore, the underlying physical mechanism and the
parameters-dependence of the spin polarization are studied.

Mesoscale and Nanoscale Physics;Biological Physics