Dispersion of parameters characterizing the Landau levels in crystals with cubic symmetry

Abstract

Broadening of the Landau levels due to the presence of a crystal cubic lattice is examined on a semiclassical basis for not too strong magnetic fields. The energies of the Landau levels remain discrete also in case of the presence of the lattice potential, but an essential broadening occurs in the momentum space of the electron motion when this motion is limited to a plane being transversal to the applied field. The broadening in the momentum space, attained without any electron-electron interaction admitted for the Landau levels, is described in terms of the band structure parameters characteristic for the presence of the magnetic field. Moreover, for a magnetic field tilted to the crystallographic axes, the broadening is dependent on the inclination angle of the field. Different crystal lattices exhibit different kinds of dispersion. In particular, for the Landau levels of tightly-bound s-electrons in a simple cubic and body-centred cubic lattice there is no dispersion in the electron gyration frequency and degeneracy number of the level area over the value of the wavevector component parallel to the magnetic field. On the other hand, this kind of dispersion exists in the case of the face-centred cubic lattice. © 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.