Metal-insulator transitions in degenerate Hubbard models and AxC60.

Abstract

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)={[ \ensuremath{\surd}x(2N-x+1) + \ensuremath{\surd}(x+1)(2N-x) ${]}^{2}$/(2N-x)}\ensuremath{\Vert}\ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{}(x)\ensuremath{\Vert}, where \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} 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}$.