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 $A_x{C}_{60}$ 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 ${\mathrm{A}}_{\mathrm{x}}{\mathrm{C}}_{60}$, at integer $x$, are Mott-Hubbard insulators and ${\mathrm{A}}_3{\mathrm{C}}_{60}$ is a strongly correlated metal.

10 pages, Revtex

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