The negative-U Hubbard model with long-range Coulomb interaction: metal-insulator transition far from half-filling.

It is shown that a metal-insulator transition can occur far from half-filling in the negative-U Hubbard model in the presence of long-range repulsive interactions. Specifically, we consider the bcc lattice at an electron concentration of 2/3 and show that a CDW insulating state exists which is energetically favoured over the relevant metallic states. The repulsive interaction plays the same role as it does in stabilizing a Wigner crystal. Despite the absence of Fermi surface nesting, the CDW insulator appears at rather small values of the interaction, preceded by a CDW semimetal at even smaller values. This places severe restrictions on the region of the parameter space where superconductivity may exist. We believe that the model will show similar behaviour for other electron densities and other lattices.