Nanotube in a periodic potential: A conveyer belt for electrons

We consider a carbon nanotube gated slightly away from the half-filled π-band, in the presence of an externally applied periodic potential. We show that the electron states can become locked by the potential when the electron density (counted from half-filling) corresponds to a rational number of electrons per potential period. At such densities, excitation gaps open up in the spectrum. When gapped, the electron system is protected from small perturbations caused by disorder, temperature and other effects. This robustness can be utilized to realize a quantized charge pump, in which a slowly moving periodic potential induces quantized current. For the gapped states with a fractional number of electrons per period, the adiabatic current will correspond to pumping on average a fraction of an electron per cycle (equivalently, to pumping at a fraction of the base frequency) as a result of electron interactions.