Interband Transitions for Metals in a Magnetic Field

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Abstract
A quantum-mechanical derivation of the frequency and magnetic field dependence of the optical reflection and transmission in metals is given. Both interband and intraband direct transitions are considered and explicit results are obtained for a model of two simple parabolic bands having energy extrema at k=0. Spin splitting is neglected. The calculated line shape is in good agreement with the magnetoreflection experiment of Brown et al. in bismuth. The results for the limiting cases of zero interband coupling or of zero magnetic field are in agreement with previous work. The study of the interband transitions in a magnetic field is shown to yield valuable information on the band structure of metals. The advantage of this method over magnetoplasma and zero-field interband studies is discussed.