Magnetic field dependence of the carrier density and magnetization in a bismuth thin film

The electrons and holes in a bismuth film placed in a transverse magnetic field assume three-dimensionally quantized energy spectra. The nonparabolicity of the conduction band and the unique effective masses result in a peculiar magnetic field dependence of the thermodynamical quantities in the film (normal to the trigonal axis). In particular, the carrier density and the magnetization exhibit unusual field dependences, quite different from that for an ordinary de Haas-van Alphen effect. Lax's energy-band model for bismuth electrons, and experimental effective masses, with modification to account for the quantum size effect, were used in the evaluations.