Magnetic Energy Levels in the Bismuth Conduction Band

The effect of other bands on the structure of the conduction band of bismuth is examined by means of perturbation theory. The unperturbed Hamiltonian is that of the Cohen-Blount two-band model as used by Lax and Mavroides and investigated more fully by Wolff. The new terms appearing in the effective-mass Hamiltonian are those already studied by Cohen in the absence of a magnetic field plus those which arise in the presence of a field because the various components of the quasimomentum do not commute. Formulas are presented for the Landau levels at $p_z=0\mathrm{}$ which can be compared with the expressions of Cohen and Blount and of Smith, Baraff, and Rowell.