  A periodic potential applied to a nanotube is shown to lock electrons into
incompressible states that can form a devil's staircase. Electron interactions
result in spectral gaps when the electron density (relative to a half-filled
Carbon pi-band) is a rational number per potential period, in contrast to the
single-particle case where only the integer-density gaps are allowed. When
electrons are weakly bound to the potential, incompressible states arise due to
Bragg diffraction in the Luttinger liquid. Charge gaps are enhanced due to
quantum fluctuations, whereas neutral excitations are governed by an effective
SU(4)~O(6) Gross-Neveu Lagrangian. In the opposite limit of the tightly bound
electrons, effects of exchange are unimportant, and the system behaves as a
single fermion mode that represents a Wigner crystal pinned by the external
potential, with the gaps dominated by the Coulomb repulsion. The phase diagram
is drawn using the effective spinless Dirac Hamiltonian derived in this limit.
Incompressible states can be detected in the adiabatic transport setup realized
by a slowly moving potential wave, with electron interactions providing the
possibility of pumping of a fraction of an electron per cycle (equivalently, in
pumping at a fraction of the base frequency).
