Landau levels for relativistic particles: Einstein–Brillouin–Keller quantization approach

The effects of a transverse magnetic field on relativistic particles in two dimensions are treated by using the semiclassical quantization rules and the role played by the spin is emphasized. The Landau levels' energies are analyzed by focusing on the square-root dependence on level index obtained for relativistic spinless particles. This result will be compared to the energies calculated for relativistic particles with spin that are governed by the Dirac equation in relativistic quantum mechanics. Then relativistic massless fermions are discussed. The approach provides a conceptual and intuitive introduction to the grounds of quantum Hall effect in carbon based nanostructures.