Influence of the Velocity Operator on Magnetoresistances in Nondegenerate Semiconductors
The investigation of the effect of a dc magnetic field on the longitudinal and transverse magnetoresistances yields useful information about the role various scattering interactions are expected to play in solids. Aliev et al  investigated the field dependence of the longitudinal and transverse magnetoresistances in the quantum limit in order to determine the influence of the band nonparabolicity and scattering inelasticity on this dependence. Hansen  proposed a correct form of the velocity operator derived from the Hamiltonian operator to show that the Hall effect is not influenced by nonparabolicity in the limit of vanishing scattering. However, when we are interested in both low and high frequency regions, the effect of scattering can not be neglected in real crystals, because there are sufficient imperfections to provide plenty of scatterings even at low temperatures. In this paper, we shall investigate the effect of the velocity operator on the magnitudes of longitudinal and transverse magnetoresistances in nondegenerate semiconductors such as n-type InSb by taking into account the effect of an electron relaxation time.
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