Electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136}$ and K$_{16}$Rb$_{8}$Si$_{136}$ clathrates

We have studied the electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136 }$and K$_{16}$Rb$_{8}$Si$_{136}$ clathrate compounds using first principles calculations. In qualitative agreement with the rigid-band model, the electronic band structures display no major modifications due to the inclusion of the alkali metal guests. The guest atom valence electrons occupy the Si$_{136}$ conduction band states, resulting in a shift of the Fermi level into the conduction band of the ``parent'' Si$_{136}$ framework. Unlike pristine Si$_{136}$, the electronic density of states of the filled clathrates show two sharply peaked structures and a dip near the Fermi level. This feature may help to qualitatively explain the temperature-dependent Knight shift observed for the NMR active nuclei in Na$_{16}$Rb$_{8}$Si$_{136}$.\footnote{S. Latturner, B. B. Iversen, J. Sepa, V. Srdanov, and G. Stucky, Phys. Rev B 63, 125403 (2001).} The phonon dispersion curves for the filled clathrates reveal low frequency, localized ``rattling'' modes for the Na (or K) and Rb guest atoms. These flat rattler modes compress the highly dispersive host acoustic mode band width. As a consequence, the rattler modes may efficiently scatter the heat-carrying host acoustic phonons, potentially suppressing the lattice thermal conductivity.