Abstract
Each electronic band of a nanotube is associated with a specific crystal orbital angular momentum, in analogy to crystal momentum. We develop the semiclassical equations of motion of electrons in such twisted Bloch bands perturbed by electric and magnetic fields. These equations demonstrate that the absorption of twisted light generates valley-dependent current along the nanotube in the presence of an external inhomogeneous magnetic field. We show that the valley-dependent current provides a venue to detect valley polarization in twisted Bloch bands.