Electronic structures of ${\mathrm{Na}}_8{\mathrm{Si}}_{46}$ and ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$

The effects of Na and Ba atoms doped into silicon clathrate compounds, ${\mathrm{Na}}_8{\mathrm{Si}}_{46}$ and ${\mathrm{Ba}}_8{\mathrm{Si}}_{46},$ on their energy-band modification have been studied. Both Na and Ba atoms occupy center sites of dodecahedral $\left({\mathrm{Si}}_{20}\right)$ and tetrakaidecahedral cages $\left({\mathrm{Si}}_{24}\right),$ irrespective of the structure of clathrate compounds. Their electronic structures are calculated within the framework of density functional theory. In ${\mathrm{Na}}_8{\mathrm{Si}}_{46}$ clathrate, the Na state is weakly hybridized with the ${\mathrm{Si}}_{46}$ conduction-band state. This weak hybridization results in almost rigid energy-band modification of pristine ${\mathrm{Si}}_{46}.$ In ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ clathrate, the conduction band is strongly modified by the Ba state. The Fermi level of ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ is located closely to a strong peak of the density of states at the conduction-band edge. Such modification causes the superconductive nature observed in the silicon clathrate doped with Ba.