S. Satpathy, V. P. Antropov, O. K. Andersen, O. Jepsen, O. Gunnarsson, and A. I. Liechtenstein
Max-Planck-Institut für Festkörperforschung, Stuttgart
We discuss the geometries of crystalline fcc C60 for three cases of directional order, the hypothetical uni-directional structure with space group Fm3, the bi-directional structure P4_2/mnm) which is the ordered version of the structure observed for alkali doped compounds at room temperature, and the quadri-directional, low-temperature structure (Pa3) of pure C60. Analytical, parameter-free expressions for the t1u-wavefunctions are derived and used to obtain analytical conduction-band Hamiltonians for all three structures. The interactions with other subbands are included in numerical tight-binding calculations with a basis of 60 radial carbon orbitals per molecule. Ab initio density functional (LDA) calculations are performed for uni-directional fcc C60 and RbC60 for different lattice constants. We use the linear muffin-tin orbitals (LMTO) method in the atomic-spheres approximation (ASA) with carefully chosen interstitial spheres. The LDA bands are compared with photoemission and inverse photoemission data for C60. For RbC60 we find that the alkali atom is fully ionized and that the doped electron occupies the t1u-band in a rigid-band like fashion. Tight-binding theory explains why, and indicates that this holds generally for An-xBxC60 with n\leq 3. The LDA calculation shows that, for a given structure, the conduction band scales uniformly in energy when, due to doping, the lattice constant a is changed. The energy scale behaves like W~d(a)\exp[-d(a)/0.58 A ] where d is the shortest distance between atoms belonging to different molecules. Both the LDA-LMTO and the tight-binding conduction-bands are well fitted by the t1u-Hamiltonians. For a=14.1 A the density of states for a conduction-band occupation of 3 electrons is 15, 17, and 21 el./(mol.eV) for the uni-, bi- and quadri-directional structures, respectively. The calculated Stoner exchange parameter is less than half the inverse density of states per spin and atom, but the Coulomb self-energy for a molecular orbital is presumably larger than the t1u-bandwidths, which are 0.52eV (uni), 0.64eV (bi), and 0.44eV (quadri) for a=14.1 A . The LDA value (0.58 A ) for the decay of the inter-molecular hopping was used together with experimental data for Tc vs. a for K_{3-x}Rb_{x}C60 compounds in the McMillan formula. The assumptions that the Coulomb-interaction mu*, the electron-phonon interaction V_{e-ph}, and the average phonon frequency omega are all independent of a were found to be inconsistent.
Phys. Rev. B 46, 1773 (1992).