Metal-Insulator Transitions: Influence of Lattice Structure, Jahn-Teller Effect, and Hund's Rule Coupling

We study the influence of the lattice structure, the Jahn-Teller effect, and the Hund's rule coupling on a metal-insulator transition in $A_n{\mathrm{C}}_{60}$ $(A=\mathrm{K},\mathrm{Rb})$. The difference in the lattice structure favors $A_3{\mathrm{C}}_{60}$ (fcc) being a metal and $A_4{\mathrm{C}}_{60}$ (bct) being an insulator, and the coupling to $H_g$ Jahn-Teller phonons favors $A_4{\mathrm{C}}_{60}$ being nonmagnetic. The coupling to $H_g$ ( $A_g$) phonons decreases (increases) the value $U_c$ of the Coulomb integral at which the metal-insulator transition occurs. There is an important partial cancellation between the Jahn-Teller effect and the Hund's rule coupling.