Interband Optical Transitions in Extremely Anisotropic Semiconductors. II. Coexistence of Exciton and the Landau Levels

Optical spectrum of a hydrogenic exciton in a uniform, static magnetic field is discussed. Based on a model previously introduced by Shinada and Sugano, i. e. the "two-dimensional model," the energy levels and the relative oscillator strengths for the "allowed case" are calculated as functions of the static magnetic field of arbitrary strength. The present work is also an extension of the previous works of Elliott-Loudon and Hasegawa-Howard, in which the magnetic field was limited to an extremely strong region (the cyclotron energy is much larger than the Rydberg energy). It is shown that the two-dimensional model can render the two concepts "exciton" and the "Landau levels" compatible. A method of extending the two-dimensional model to the three dimension is also given.