Superconductivity and Density Waves in High Dimensions

Density and pairing responses are studied for the Holstein molecular crystal model. The charge density wave (CDW) and the superconductivity (SC) instabilities of the normal phase are investigated. Analytical results are obtained for small electron-phonon coupling in a simple cubic lattice in the limit of large dimensionality (d = ∞). Near half-filling the dominant instability is a CDW, due to nesting at q = (π, π,...). For larger deviations from half-filling the CDW becomes incommensurate in a narrow filling range and finally disappears. Then the SC instability dominates.