Scattering Theory for the Metamorphism of Van Hove Singularities in the Optical Spectra of Solids

Abstract

The metamorphism of Van Hove singularities in the optical absorption spectra of solids is described in terms of the scattering theory. The infrared absorption of phonons induced by an impurity ion in a nonpolar crystal and the interband absorption of electrons in a semiconductor are discussed in detail, in which scattering of phonons by an impurity ion and that of the relative motion of an electron-hole pair by the electron-hole interaction are taken into account. The metamorphism of Van Hove singularities occurs in the optical spectra due to the interference between incoming and scattered waves, and is described by two phases η 1 and η 2 . η 1 is the phase shift of scattering, and η 2 is the optical structure factor of the scattering potential. Phonon sidebands of localized electron or phonon absorption, with the metamorphism of their Van Hove singularities, can be treated in the same form.