Metal-Insulator Transitions in Degenerate Hubbard Models and A$_x$C$_{60}$

Abstract

Mott-Hubbard metal-insulator transitions in $N$-fold degenerate Hubbard models are studied within the Gutzwiller approximation. For any rational filling with $x$ (integer) electrons per site it is found that metal-insulator transition occurs at a critical correlation energy $U_c(N,x)=U_c(N,2N-x)=\gamma(N,x)|\bar{\epsilon}(N,x)|$, where $\bar{\epsilon}$ is the band energy per particle for the uncorrelated Fermi-liquid state and $\gamma(N,x)$ is a geometric factor which increases linearly with $x$. We propose that the alkali metal doped fullerides $A_xC_{60}$ can be described by a 3-fold degenerate Hubbard model. Using the current estimate of band width and correlation energy this implies that most of ${\rm A_xC_{60}}$, at integer $x$, are Mott-Hubbard insulators and ${\rm A_3C_{60}}$ is a strongly correlated metal.