Structural and electronic properties of germanium clathrates ${\mathrm{Ge}}_{46}$ and ${\mathrm{K}}_8{\mathrm{Ge}}_{46}$

The structural and electronic properties of germanium clathrates ${\mathrm{Ge}}_{46}$ and ${\mathrm{K}}_8{\mathrm{Ge}}_{46}$ are studied by first-principles calculations within the local-density approximation. The equilibrium structures are obtained by ab initio pseudopotential calculation combined with dynamic minimizations. The clathrate structure is found as a low-energy phase for germanium. The electronic band structures for ${\mathrm{Ge}}_{46}$ clathrates are calculated and the band gap is found to be considerably larger than that of the diamond phase. Due to the effect of pentagonal rings, strong similarity in electronic properties between clathrate and ${\mathrm{Ge}}_{24}$ fullerene structure are found. The effect of doping clathrate cages with metal atoms are examined. The ${\mathrm{K}}_8{\mathrm{Ge}}_{46}$ clathrate is found to be metallic with the conduction bands only slightly modified by K dopants.