High-field magnetoresistance of nonparabolic-band and bismuth-type metals

A quantum-mechanical study has been made of the galvanomagnetic effect including intraband elastic scattering for electrons in bismuth-type metals with ellipsoidal-nonparabolic dispersion relation. The analysis is based on the Kubo formulas for static electrical conductivity. The magnetoconductivity tensor in the strong-magnetic-field region has been worked out in the general case where the magnetic field is in an arbitrary direction with respect to the Fermi ellipsoid. The relative- and center-coordinate operators for the electron cyclotron motion are properly redefined in order to accommodtate the nonzero off-diagonal effective masses resulting from the arbitrariness in direction of the applied magnetic field. The difficulty arising from the nonparabolicity in the dispersion relation is also overcome, thus all of the magnetoconductivity tensor elements can be obtained in compact forms when the magnetic field is sufficiently strong. An explicit curve for the transverse magnetoresistance of bismuth in crossed electric and magnetic fields has been computed. We find that, by using electron=2.3×10-10 sec and hole=1.2×10-10 sec, our computed result is in reasonable agreement with some experimental data taken at T=4.2°K.