Theory of Lattice Raman Scattering in Insulators

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Abstract
The theory of Raman scattering by phonons in perfect insulator crystals is developed here. The Hamiltonian for the interacting system of electrons, phonons, and photons is written in second-quantized form, and a canonical transformation is performed to remove the lowest-order interactions. In the resulting transformed Hamiltonian, the terms causing Raman scattering can be identified. The basic electron-system eigenstates are taken in the Wannier exciton representation, including bound and continuum states. The frequency dependence of the components of the Raman tensor is obtained for single-phonon and two-phonon overtone scattering. As a function of incident photon energy, the Raman tensor has poles at energies corresponding to creation of quasiparticles (e.g., virtual excitons). This produces a particularly important effect in resonance Raman scattering, where the creation of virtual excitons dominates the scattering process. Some numerical estimates for single and overtone resonant-Raman-scattering efficiencies are given for CdS and GaAs, and are compared with available experiments. The use of the resonance Raman effect as a probe of quasiparticles is suggested.

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