  It is shown that a periodic potential applied to a nanotube can lock
electrons into incompressible states. Depending on whether electrons are weakly
or tightly bound to the potential, excitation gaps open up either due to the
Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via
pinning of the Wigner crystal. Incompressible states can be detected in a
Thouless pump setup, in which a slowly moving periodic potential induces
quantized current, with a possibility to pump on average a fraction of an
electron per cycle as a result of interactions.
