Metal-insulator transitions in degenerate Hubbard models and AxC60.

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 Uc(N,x) = Uc(N, 2N − x) = γ(N,x)|ǭ(N,x)|, where ǭ is the band energy per particle for the uncorrelated Fermi-liquid state and γ(N,x) is a geometric factor which increases linearly with x. We propose that the alkali metal doped fullerides AxC60 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 AxC60, at integer x, are Mott-Hubbard insulators and A3C60 is a strongly correlated metal. PACS numbers: 71.10.+x,71.30.+h,74.70.W Typeset using REVTEX 1 The discovery of superconductivity in A3C60 [1] has spurred great interest in alkali metal doped fullerides [2]. Beside A3C60, stable phases such as Rb1C60, Na2C60, K4C60 were synthesized [2,3]. One unusual property is that except A3C60 all integer x phases are found to behave like insulators [4]. This contradicts the band structure calculations which imply that all of them are metals due to the 3-fold degeneracy of the t1u molecular orbitals which forming the conduction bands [5]. In this letter we show that the strong (compared with the band width) intramolecular electron-electron correlation is responsible for this unusual property. The results we have obtained also shed light on the instability of the non-integer x phases [6]. The existence of strong correlation in pure C60 is supported by spectroscopy experiments. Photoemission shows an insulating gap of 2.6eV, while the photo-conductivity and absorption indicate excitation at 1.6eV. This discrepancy is interpreted as due to strong correlation which results in a large excitonic binding energy. The estimated correlation energy U ∼ 1eV [4,7,8] is much larger than the conduction band width W ∼ 0.2− 0.4eV [5,10]. Thus, it has been suggested that that A3C60 is a Mott-Hubbard insulator and the superconducting phase is non stoichiometric [7]. However, structural, transport and spectroscopic measurements show that the superconducting phase is stoichiometric and there is no evidence of insulating behavior in A3C60. Even more interesting is that for x 6= 3 integer stoichiometric phases no metallic behavior have been observed so far. Therefore neither a simple Hubbard model which prefers insulating at half filling (x = 3), nor the simple band filling model which predict metallic behavior for all phases, can explain the unusual metal-insulator transitions observed. Clearly the 3-fold degeneracy of the conduction band can not be neglected. This leads us to study the general N -fold degenerate Hubbard model at rational fillings. We find that the unusual metal-insulator transitions observed can be understood in term of Mott-Hubbard transition in the degenerate Hubbard model. It is found that for a general N -fold degenerate Hubbard model at rational filling x/2N , where the average number of electrons per site (x) is an integer, the metal-insulator transition occurs at a critical Uc which increases with both 2 x and N . Uc is found to be the largest at half filling x = N for a given degeneracy N (except N = 2). Therefore it is possible that the system is a metal at half filling while insulating away from it. Our results lay a solid theoretical foundation for the interpretation that AxC60 are either Mott-Hubbard insulators or strongly correlated metals and provide a rationale to understand the unusual metal-insulator transitions in this family of materials and molecular metals in general. Consider the general N -fold degenerate Hubbard model with the correlation energy U independent of orbitals and spins