Low-field magnetoconductivity of metals with ellipsoidal-nonparabolic band structure

A simple method has been worked out for theoretical analysis of the galvanomagnetic tensor elements for metals with ellipsoidal-nonparabolic (ENP) band structure in low magnetic fields. Using a drift-momentum approach, simple algebraic calculation leads to a compact form of expression for the magnetoconductivity tensor of ENP electrons in the general case when the magnetic field is in an arbitrary direction with respect to the Fermi ellipsoid. This model may be easily extended to the case when the relaxation times are anisotropic. Thus, application of the method to the bismuth-type metals can be readily made. The results obtained indicate that 1) our general expression can easily be reduced to that of a previous calculation on the galvanomagnetic effects in Bi with fields along the principal symmetry directions; 2) the lowest-order expansion in 1/Ωτ agrees with our detailed calculation of magnetoconductivity in strong fields; and 3) when the appropriate limit is taken, our result is in accord with an earlier published result for ellipsoidal-parabolic electrons.