Coexistence of Local and Band Characters in the Absorption Spectra of Solids I. Formulation

The problem of coexistence of the local and band aspects in the fundamental absorption spectra (or the impurity-induced infrared absorption of lattice vibrations) is formulated with the use of the Green's function method. By a suitable decomposition of the hamiltonian of the electron-hole relative motion (or the dynamical matrix for the lattice vibrations), one can derive a line shape expression in which coexist the both aspects, namely, the metastable excitons (or the quasi-local modes) on the one hand and the Van Hove singularities on the other hand. Their interference results in the antiresonance of the quasi-local states and the metamorphism of Van Hove singularities.