Total dielectric function: Algebraic sign, electron-lattice response, and superconductivity

The interaction between two test charges in a solid can be described in terms of a total dielectric function that includes electronic and lattice polarization. Crystal stability requires the eigenvalues of ε^-1 to be {≤}1. Some implications for superconductivity are discussed. A total dielectric function for the electron-lattice system is derived in the mean-field approximation and its inverse is explicitly constructed. The low-lying poles of ε^-1 give the correct phonon frequencies as determined by the usual dynamical matrix.