Simple Model of Electronic Correlation in Insulators

To facilitate calculation of the effects of electron-electron interaction in insulators, a dielectric model is developed analogous to one used by Overhauser to discuss correlation in metals. In this model the dynamical many-electron problem is replaced by a field-theoretic problem in which an electron interacts with a "plasmon" field representing the valence-charge distribution. For small wave vector →q the plasmon dispersion ω(→q) approaches the bulk plasma frequency; at large →q, ω(→q)→→q²2m, corresponding to single-particle excitations. To determine the electron-plasmon coupling Poisson's equation and the sum rule on oscillator strength are employed. Calculated self-energies of an electron (or hole) due to correlation are large, typically 1/3 Ry, though substantially reduced by recoil effects if the electron mass is small. Exchange effects lead to further reduction. The crucial importance of short-range (large-→q) dielectric behavior is emphasized.