Excitonic Collective Mode and Negative Compressibility in Electron Liquids

A highly self-consistent theory maintaining the exact functional relations between the elec-tron self-energy and the vertex part is employed to calculate the dielectric function ε(q, ω) very accurately in the homogeneous electron gas in two- and three-dimensions. By investi-gating the full dynamical properties of ε(q, ω) thus obtained, we find that the softening of excitonic collective modes is responsible for making the compressibility of the system nega-tive at sufficiently low densities. KEY WORDS: negative compressibility; vertex correction; excitonic effect; dielectric function; electron gas