Abstract
From the classical equation of motion a conductivity tensor is derived for a bound electron in a dc external magnetic field. Then the conductivity for a circularly polarized wave is obtained, which is expanded in terms of the magnetic field. With the appropriate form of the oscillator strength for the interband transitions, the conductivity components are evaluated for the zeroth, first, and second power of the magnetic field over the two energy bands for the direct and the indirect transitions. The results are used to obtain expressions for the interband Faraday rotation and the Voigt phase shift in the limits of $\ensuremath{\omega}<{\ensuremath{\omega}}_{g}$ and $\ensuremath{\omega}>{\ensuremath{\omega}}_{g}$, where $\ensuremath{\omega}$ is optical frequency and ${\ensuremath{\omega}}_{g}$ the frequency corresponding to the energy gap. In the latter case oscillatory behavior is described by the expression near the frequency of singularities with a loss term in the form of relaxation time $\ensuremath{\tau}$.
Published Version
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