Theory of Raman scattering from charge-density-wave phonons

A recent microscopic theory of two-phonon Raman scattering by anomalous phonons in transition-metal compounds is extended to one-phonon scattering from phonons associated with a charge density wave (CDW). To lowest order in the CDW distortion the two-phonon results can be used directly. For layered transition-metal dichalcogenides the Raman intensities of the CDW modes result mainly from intralayer interactions. To understand observed intensities in $2H$-TaSe₂ anharmonicity and higher-order Raman coefficients are included within a Landau theory. For stronger distortions a general theory is possible, but a simple solution can only be given for a very simple model with a single conduction band and a single CDW wave vector. The simple solution for the Raman amplitude can be made analytic for the case of one dimension. Some conclusions are also drawn for more general cases.