  We analyse the appearance of a mechanical torque that acts on a chiral
molecule: a single-stranded DNA, in which the spin-orbit interaction is
expected to induce a spin-selectivity effect. The mechanical torque is shown to
appear as a result of the non-conservation of the spin current in the presence
of the spin-orbit interaction. Adopting a simple microscopic model Hamiltonian
for a chiral molecule connected to source and drain leads, and accounting for
the mechanical torque acting on the chiral molecule as the back action on the
electrons traversing the molecule, we derive the spin continuity-equation. It
connects the spin current expressed by a Landauer-type formula and the
mechanical torque. Thus, by injecting a spin-polarized current from the source
electrode, it is possible to generate a torque, which will rotate the DNA
molecule.
