Pressure dependence of the band structure, density of states, Fermi surfaces, and optical properties of superconducting ${\mathrm{K}}_3$${\mathrm{C}}_{60}$

The electronic, the structural, and the optical properties of the fcc ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ crystal and their dependence on isotropic pressure are studied theoretically by means of first-principles local-density calculations. The calculated equilibrium volume and the pressure coefficients are in good agreement with experimental measurements. The changes in the band structure, the density of states (DOS), the Fermi-surface topology, and the optical-absorption spectrum with pressure are analyzed in detail and compared with other recent theoretical calculations and available measurements. With an increased pressure, the DOS at the Fermi level decreases, the gap diminishes, and the bands widen and eventually merge. The change in the band structure has resulted in the merging of the absorption peaks in the optical spectrum and in the decrease of the static dielectric constant. The linear dependence of the DOS at the Fermi level due to pressure is found to have a smaller slope than that due to the expansion of the lattice by introducing different alkali-metal intercalates of varying ionic radii. The pressure dependence of the superconducting temperature in ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ is estimated by the use of the McMillan formula and a set of optimized parameters obtained earlier in the study of ${\mathit{T}}_{\mathit{c}}$ in five alkali-metal-doped fullerites. The agreement with the measured data is not as good as that for the other alkali-metal-doped fullerites but shows the correct trend. The effective Coulomb repulsion in ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ is also estimated and found to be small.