  Chiral-induced-spin-selectivity of electron transport and its interplay with
DNA's mechanical motion is explored in a double stranded DNA helix with
spin-orbit-coupling. The mechanical degree of freedom is treated as a
stochastic classical variable experiencing fluctuations and dissipation induced
by the environment as well as force exerted by nonequilibrium, current-carrying
electrons. Electronic degrees of freedom are described quantum mechanically
using nonequilibrium Green's functions. Nonequilibrium Green's functions are
computed along the trajectory for the classical variable taking into account
dynamical, velocity dependent corrections. This mixed quantum-classical
approach enables calculations of time-dependent spin-resolved currents. We
showed that the electronic force may significantly modify the classical
potential which, at sufficient voltage, creates a bistable potential with
considerable effect on electronic transport. The DNA's mechanical motion has a
profound effect on spin transport; it results in chiral-induced spin
selectivity increasing spin polarisation of the current by 9% and also
resulting in temperature-dependent current voltage characteristics. We
demonstrate that the current noise measurement provides an accessible
experimental means to monitor the emergence of mechanical instability in DNA
motion. The spin resolved current noise also provides important dynamical
information about the interplay between vibrational and spin degrees of freedom
in DNA.
