T-C Dependence on Hubbard U in the Fullerenes

Pair formation occurs when the free energy for charge disproportionation is negative, i.e., U < 0. The Mott-Hubbard energy U is here approximated by U = I - A-1/R, where I - A > 0 is the difference between ionization energy and electron affinity, and R is the distance between the lattice sites. -1/R (atomic units) is the particle-hole attraction after charge separation in the case of two C-60 ions, the much needed negative term. In the case of alkali C-60 salts of type A(3)C(60), the attractive term 1 /R is the smallest for the largest ion A(+), i.e., Cs+. Hence, U is increasing with the lattice constant R, i.e., with the size of the alkali ion. Lack of superconductivity in Cs3C60 can be interpreted as U > 0 for this salt, while U < 0 for the other A(3)C(60). This is also consistent with the antiferromagnetic ground state for Cs3C60 at ambient pressure, and superconductivity for pressures > 4 kbar