A Theory of the Magneto-Optical Absorption

Abstract

A theory of the magneto-optical absorption is developed by means of the Luttinger and Kohn theory of the effect of magnetic field on the energy bands in the case of a simple band model. The main purpose is to study the absorption line shape. As the width of the ab­ sorption line we get a value which agrees with experiment. It does not exhibit appreciable dependence on the magnetic field and temperature. The absorption coefficient in the absence of a magnetic field is also discussed. Recently, optical absorption experiments in semi-conductors have been performed in a strong magnetic field. These results show that absorption edges shift to shorter wave-length side in proportion to the magnetic field and the absorption spectrum shows an oscillation which is not observed in the absence of a magnetic field. These facts can be interpreted as the optical absorption which is accompanied with transitions of electrons between Landau levels of the valence band and of the conduction band. This is the oscillatory magneto-optical absorption effect_ll In this effect we are interested in i) positions of absorption peaks, ii) selec­ tion rules and iii) absorption line shapes, which are determined by level scheme, symmetry of band structure and scattering mechanism of carriers. Elliott et al,2l discussed the problems i) and ii). In this paper the electron-phonon interaction is taken into account and the absorption line shape is discussed as the main prob­ lem. We aim to gain some information about the relation between absorption line shapes and scattering mechanisms in the case of a strong magnetic field. In order to avoid the complexity, treatment is done for a simple spherical band model. In § 2, we shall make general considerations. In § 3, we shall discuss the absorp­ tion coefficient by. taking account of phonon effects. We will give numerical ex­ amples and discussions in § 4.