  In this study, we theoretically show that in a helical crystal, a current is
induced by chiral phonons representing the microscopic local rotation of atoms.
By treating the rotational motion as a perturbation, we calculate the
time-dependent current by using the adiabatic Berry phase method. The time
average of the current along the helical axis becomes finite in the metallic
phase but it vanishes in the insulating phase. On the other hand, the current
in the hexagonal plane changes with time, but its time average vanishes due to
the threefold rotation space-time symmetry. We show that the time evolutions of
the current follow the space-time symmetries of the helical systems. Moreover,
we explain the reason for the vanishing of the time average of the current in
the insulating phase from the aspect of the Chern number in the parameter
space.
