Effect of Band Structure on Longitudinal Magnetoresistance in Semimetals and Semiconductors

Abstract

The effect of the Cohen nonellipsoidal nonparabolic (NENP) band structure on the propagation of ultrasound in a semimetal such as bismuth in the presence of a dc magnetic field is investigated by using a quantum-mechanical treatment which is valid at high frequencies and in strong magnetic fields. It is found that the longitudinal magnetoresistance oscillates with the dc magnetic field. This dependence on the dc magnetic field arises from the nonlinear effect of the energy bands owing to the NENP model for the energy band structure of bismuth. We compare these results with those of the ellipsoidal parabolic (EP) band structure of bismuth. We also present numerical results for the nondegenerate and degenerate semiconductors like n-type InSb. It is found that the longitudinal magnetoresistance in the nondehenerate case changes with the dc magnetic field only for the nonparabolic band structure. In the degenerate case, however, the longitudinal magnetoresistance for the parabolic and nonparabolic band structures will oscillate with the dc magnetic field. These oscillations are interpreted as the so-called "giant quantum oscillations " which occur in a degenerate electron gas.