Conduction-band structure of alkali-metal-dopedC60

We discuss the geometries of crystalline fcc ${\mathrm{C}}_{60}$ for three cases of directional order, the hypothetical undirectional structure with space group Fm3¯, the bidirectional structure (P$4_2$/mnm) which is the ordered version of the structure observed for alkali-metal-doped compounds at room temperature, and the quadridirectional, low-temperature structure (Pa3¯) of pure ${\mathrm{C}}_{60}$. Analytical, parameter-free expressions for the ${\mathit{t}}_{1\mathit{u}}$ wave functions 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 [local-density approximation (LDA)] calculations are performed for unidirectional fcc ${\mathrm{C}}_{60}$ and ${\mathrm{RbC}}_{60}$ for different lattice constants. We use the linear-muffin-tin-orbitals (LMTO) method in the atomic-spheres approximation with carefully chosen interstitial spheres. The LDA bands are compared with photoemission and inverse photoemission data for ${\mathrm{C}}_{60}$. For ${\mathrm{RbC}}_{60}$ we find that the alkali-metal atom is fully ionized and that the doped electron occupies the ${\mathit{t}}_{1\mathit{u}}$ band in a rigid-band-like fashion. Tight-binding theory explains why, and indicates that this holds generally for ${\mathit{A}}_{\mathit{n}\mathrm{-}\mathit{x}}$ ${\mathit{B}}_{\mathit{x}}$ ${\mathrm{C}}_{60}$ with n≤3.