Magnetic field dependence of the energy gap in nanotubes

The dependence of the energy gap in the band structure of a carbon nanotube on the flux of an external uniform magnetic field is studied in the framework of the zero-range potential method. Taking into account a renormalization procedure for the coupling constant of the zero-range potential, we obtain an estimate for the maximal gap between the conductivity band and the valence one; this estimate is closer to experimental data when compared to the value given by the tight-binding approximation. It is shown numerically that decreasing the diameter of nanotubes breaks down the flux periodicity of the gap structure.