  Recent theoretical and experimental works on carbon nanotubes (CNTs) have
revealed that spin-orbit interaction (SOI) is more robust than it was thought.
Motivated by this, we investigate the SOI in helically coiled CNTs.
Calculations are performed within the tight-binding model with the inclusion of
a four-orbital basis set; thereby the full symmetry of the helical lattice and
the hybridization of $\pi $\ and $\sigma $ bands are considered. By virtue of
unitary transformation and perturbation approach, we obtain the analytic
solution for the torsion-dependent SOI in helically coiled CNTs. Due to the
enhancement of curvature and torsion, the calculated SOI values reach the order
of meV which has been confirmed by \textit{ab initio} electronic structure
calculation.
