Abstract
The effect of phonons on the density of states near a critical point in the band structure of an insulator or semiconductor is investigated. Dyson's equation is solved assuming that the electron-phonon coupling parameter is independent of wave vector. Electron phonon-vertex and central-cell corrections are negligible. It is concluded that so long as the critical point is not near threshold, the phonons broaden the structure associated with the critical point, but introduce no structure of their own. Therefore, electron-phonon self-energies cannot explain the anomalous structure observed in the vicinity of saddle points in a number of semiconductors.
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