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.

Figure 1

Electron energy spectrum for a (10,0) zigzag nanotube in a perpendicular magnetic field corresponding to $R/a_B=1$ calculated using the tight-binding Hamiltonian (blue dashed lines) and Eq. (25) (red solid lines). Black dotted lines show the electron energy spectrum of the same nanotube without magnetic field.