Microscopic theory of electron-phonon interaction in insulators or semiconductors

P. Vogl

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A unified treatment of the electron-phonon interaction matrix M in insulators (or semiconductors at low temperatures) is given in terms of the complete linear electron response within the adiabatic approximation. The effective electron-one-phonon (el-ph) potential M which is constructed, analogously to metals, as a screened vertex-corrected renormalized (bare) ion potential is defined, including all many-body corrections. We derive the small-wave-vector (q→) limit of M leading to multipole as well as short-range contributions by separating out the electron response for fixed macroscopic electric field and using the analytical properties of the inverse dielectric tensor ε-1. We obtain explicit expressions for all standard types of el-ph couplings in terms of microscopic quantities in principle calculable from band structure. The main results of Lawaetz are rederived and new-indirectly induced-multipole terms are obtained. A new quadrupole sum rule for ε is proved which guarantees, together with the already known acoustic sum rule, the well-known behavior of the acoustic scattering potential as a function of q in the elastic limit. An effective el-two-ph scattering is investigated; further sum rules are proved representing constraints on a nonlinear response function.

Original languageEnglish
Pages (from-to)694-704
Number of pages11
JournalPhysical Review B
Issue number2
StatePublished - 1976
Externally publishedYes


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