Electronic structure and phase stability of Yb-filled skutterudite CoSb$_3$ from first principles

Filling the large voids in the crystal structure of the skutterudite CoSb$_3$ with rattler atoms $R$ provides an avenue for both increasing carrier concentration and disrupting lattice heat transport, leading to impressive thermoelectric performance. While the influence of $R$ on the lattice dynamics of skutterudite materials has been well studied, the phase stability of $R$-filled skutterudite materials and the influence of the presence and ordering of $R$ on the electronic structure remain unclear. Here, focusing on the Yb-filled skutterudite Yb$_x$Co$_4$Sb$_{12}$, we employ first-principles methods to compute the phase stability and electronic structure. Yb-filled CoSb$_3$ exhibits a mild tendency for (1) phase separation into Yb-rich and Yb-poor regions and (2) chemical decomposition into Co--Sb and Yb--Sb binaries (i.e., CoSb$_3$, CoSb$_2$, and YbSb$_2$). Due to the small energetic magnitude of such instabilities, configurational entropy is expected to stabilize single-phase solid solutions at reasonable synthesis temperatures, in agreement with experiments. Filling CoSb$_3$ with Yb increases the band gap, enhances the carrier effective masses, and generates additional low-energy "emergent" conduction band minima, known as band convergence. The explicit presence of $R$ is responsible for the band convergence, though the rattler ordering does not strongly influence the electronic structure. The emergent conduction bands are spatially localized in the Yb-rich regions, unlike the delocalized electronic states at the Brillouin zone center that form the band edges for the unfilled skutterudite.