Effect of a magnetic field on the phonon-assisted two-photon absorption in semiconductors

The theory of the phonon-assisted two-photon transitions in a magnetic field is developed by means of perturbation theory. Three different band models have been introduced. The electronic transitions are defined by (i) interband-interband indirect transitions in the four-band model, (ii) interband-intraband indirect transitions in the three-band model, and (iii) intraband-intraband indirect transitions in the two-band model. These models differ from each other by the number of bands, the type of the photon matrix elements and the Landau selection rules. The result shows that by increasing the value of the magnetic field, the absorption co-efficient adopting the two-band model is strongly increased, but for a fixed value of the field the four-band model gives the largest contribution.