Metal-insulator transitions in degenerate Hubbard models andAxC60

Analytic results for Mott-Hubbard metal-insulator transitions in N-fold degenerate Hubbard models are obtained using the Gutzwiller approximation. It is found that for any commensurate filling with integer (x) electrons per site, there exists a metal-insulator transition at the critical correlation energy ${\mathit{U}}_{\mathit{c}}$(N,x)={[ √x(2N-x+1) + √(x+1)(2N-x) ${]}^2$/(2N-x)}‖ε¯(x)‖, where ε¯ is the energy per particle in the absence of correlation. ${\mathit{U}}_{\mathit{c}}$ increases with x reaching the maximum at the half filling x=N. Therefore, it is possible for a system to be metallic at half filling and insulating away from half filling. This provides an explanation for the unusual metal-insulator transitions observed in fullerides ${\mathit{A}}_{\mathit{x}}$ ${\mathrm{C}}_{60}$.