Bloch electrons of a carbon nanotube in a perpendicular magnetic field

The Peierls substitution in the energy functions of a carbon nanotube's sub-bands is carried out for a carbon nanotube of arbitrary chiral indices subjected to a perpendicular uniform magnetic field. The Peierls substitution represents a zeroth-order term of the asymptotically convergent power series in the magnetic field. It provides a very good approximation for the electron energy spectrum of a carbon nanotube subjected to a perpendicular uniform magnetic field, for magnetic fields currently accessible in laboratories.