Electron-phonon interaction in the solid form of the smallest fullerene C${}_{20}$

Abstract

The electron-phonon coupling of a theoretically devised carbon phase made by assembling the smallest fullerenes C${}_{20}$ is calculated from first principles. The structure consists of C${}_{20}$ cages in an {\it fcc} lattice interlinked by two bridging carbon atoms in the interstitial tetrahedral sites ({\it fcc}-C${}_{22}$). The crystal is insulating but can be made metallic by doping with interstitial alkali atoms. In the compound NaC${}_{22}$ the calculated coupling constant $\lambda /N(0)$ is 0.28 eV, a value much larger than in C${}_{60}$, as expected from the larger curvature of C${}_{20}$. On the basis of the McMillan's formula, the calculated $\lambda$=1.12 and a ${\mu }^{\ast }$ assumed in the range 0.3-0.1 a superconducting T${}_c$ in the range 15-55 K is predicted.

7 pages