## Abstract

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 language | English |
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Pages (from-to) | 694-704 |

Number of pages | 11 |

Journal | Physical Review B |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - 1976 |

Externally published | Yes |