Landau Levels and Magneto-Optic Effects at Saddle Points

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Abstract
We give a quantum-mechanical treatment for the eigenstates of electrons near saddle points of the energy bands in the presence of a constant magnetic field. We find that Landau-type levels exist depending on the orientation of the magnetic field. Correspondingly, we find peaks in the interband transition probabilities and discuss selection rules on the Landau quantum numbers. We show the behavior of the optical constants for a chosen direction of the magnetic field, and indicate experimental consequences.