The Hubbard model is extended to include long-range Coulomb interactions between electrons on different atomic sites. This results in a screening of the effective correlation energy by free carriers. Both the cases of an integral number of electrons per atom and a general electronic density are considered. The electronic free energies of both insulating and metallic states for finite bandwidths are calculated and compared. These results are used to generate complete phase diagrams as functions of temperature and bandwidth. A wide range of electronic behavior can be understood by use of the model. For certain materials, insulator-to-metal transitions are predicted as the temperature is increased. However, for somewhat larger bandwidths, a metallic ground state is present and two transitions are predicted: metal-to-insulator and, at a still higher temperature, insulator-to-metal. The model is used to analyze the anomalous transport properties of the ${\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{\mathrm{S}}_2$ system.

• Received 30 November 1978

DOI:https://doi.org/10.1103/PhysRevB.20.4044