Landau levels and edge states in carbon nanotubes: A semiclassical approach

Abstract

The effects of a transverse magnetic field on the quantum mechanical magnetoelectronic structure of carbon nanotubes (CNs) are investigated, making use of the Einstein Brillouin Keller (EBK) semiclassical quantization. This approach, which is based on Dirac fermions moving on a cylindrical surface, gives detailed knowledge of the correspondence between the classical paths (cyclotron orbits localized at the top or the bottom of the CN, edge-skipping orbits restricted on the flanks of the tube, and traversing trajectories with charges rotating around the circumference) and the quantized EBK single-electron energies. The semiclassical approach also allows us to clearly distinguish within the magnetosubbands the geometrical effects of the curvature from the lattice effects and to estimate analytically the threshold field for the semiconducting-metallic transition in CNs.