Electronic structure of ${\mathrm{Si}}_{46}$ and ${\mathrm{Na}}_2$${\mathrm{Ba}}_6$${\mathrm{Si}}_{46}$

We study solids of ${\mathrm{Si}}_{20}$ fullerenes, ${\mathrm{Si}}_{46}$ and ${\mathrm{Na}}_2$${\mathrm{Ba}}_6$${\mathrm{Si}}_{46}$, in the framework of density-functional theory. The electronic structure of ${\mathrm{Si}}_{46}$ is remarkably different from that of the diamond Si lattice due to its pentagonal network. The valence-band top becomes deeper, resulting in a narrow valence-band width and a wide fundamental gap. Also, another gap appears within the valence bands. In the Na- and Ba-codoped phase, Ba states show strong hybridization with ${\mathrm{Si}}_{46}$ states giving a very high Fermi-level density of states, which should be of essential importance for the superconductivity observed in ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{Ba}}_{\mathit{y}}$${\mathrm{Si}}_{46}$.