On the basis of an analysis of a 3/4-filled two-dimensional (2D) extended Hubbard model under the fluctuation-exchange approximation, we find Coulomb frustrated phase separation (PS) in a region of nonzero temperature, where the quantum critical phen
omenon of charge ordering (CO) dominates. In quasi-2D organic conductors on the verge of CO, this frustrated PS provides a mechanism for generating spatial inhomogeneity, which is characterized by an extremely slow relaxation and an intermediate length scale.
By treating the electron-ion interaction as perturbation in the first-principles Hamiltonian, we have calculated the density response functions of a fluid alkali metal to find an interesting charge instability due to anomalous electronic density fluc
tuations occurring at some finite wave vector ${bi Q}$ in a dilute fluid phase above the liquid-gas critical point. Since $|{bi Q}|$ is smaller than the diameter of the Fermi surface, this instability necessarily impedes the electric conduction, implying its close relevance to the metal-insulator transition in fluid alkali metals.
