Nonlinear electromagnetic response of bloch electrons in a magnetic field. II-two-band model for semi-conductors

Abstract

Following the general formulation developed in part I of this work, the linear and nonlinear electromagnetic responses of small-band-gap semi-conductors, in the presence of a small d.c. magnetic field, are studied in the electric-dipole approximation. A two-band model with an isotropic inverse effective-mass tensor at k=0 is used to find the effect of nonparabolicity of conduction and valence bands on the linear and third-order responses. The solid is assumed to have inversion symmetry. The third-order induced-current density describes the fundamental process of scattering of light by light in the medium. Even in the low-frequency approximation, with low concentrations of carriers in the non-parabolic conduction band, our results differ considerably from those obtained in a semi-classical one-band calculation.