  It is widely admitted that the helical conformation of certain chiral
molecules may induce a sizable spin selectivity observed in experiments. Spin
selectivity arises as a result of the interplay between a helicity-induced
spin-orbit coupling and electric dipole fields in the molecule. From the
theoretical point of view, different phenomena might affect the spin dynamics
in helical molecules, such as quantum dephasing, dissipation and the role of
metallic contacts. Previous studies neglected the local deformation of the
molecule about the carrier thus far, but this assumption seems unrealistic to
describe charge transport in molecular systems. We introduce an effective model
describing the electron spin dynamics in a deformable helical molecule with
weak spin-orbit coupling. We find that the electron-lattice interaction allows
the formation of stable solitons such as bright solitons with well defined spin
projection onto the molecule axis. We present a thorough study of these bright
solitons and analyze their possible impact on the spin dynamics in deformable
helical molecules.
