  We show that an electrical shift current is generated when electrons are
photoexcited from the valence to conduction bands on a BN nanotube. This
photocurrent follows the light pulse envelope and its symmetry is controlled by
the atomic structure of the nanotube. We find that the shift current has an
intrinsic quantum mechanical signature in which the chiral index of the tube
determines the direction of the current along the tube axis. We identify
discrete lattice effects in the tangent plane of the tube that lead to an
azimuthal component of the shift current. The nanotube shift current can lead
to ultrafast opto-electronic and opto-mechanical applications.
