Role of the van Hove singularity on the critical temperature of doped fullerenes

We investigate the role played by van Hove singularity (vHs) on the optimization of the value of $T_c$ in doped fullerense ${\mathrm{C}}_{60}{\mathrm{K}}_3$ by employing a first-principles self-consistent full-potential linear muffin-tin orbital method in local-density approximation. For ${\mathrm{C}}_{60},$ the computed band structure shows an insulating behavior with a direct band gap at the symmetry point X. The valence band originates from ${\mathrm{C}}_{60}$ molecule $h_u$ states whereas the conduction band originates from the molecular $t_{1u}$ states. In ${\mathrm{C}}_{60}{\mathrm{K}}_3$ the two types of K(1) and K(2) atoms occupy tetrahedral and interstitial positions, respectively. The band structure is very nearly similar to that of pure ${\mathrm{C}}_{60}.$ The three extra K electrons fill the $t_{1u}$ band up to half, making ${\mathrm{C}}_{60}{\mathrm{K}}_3$ conducting. The K-induced states appear mostly in the conduction-band region. We observe a saddle point leading to vHs in the vicinity of the symmetry point L slightly shifted towards the Γ point, very near the Fermi level. The saddle point lies exactly at the Fermi level for a lattice constant of 14.51 Å (a 5% dilation) for which the highest value of $T_c$ may be detected in the experiments.