Optical and thermoelectric properties of Tl-filled CoSb$_3$ skutterudites from first-principles

Filled skutterudite antimonides have attracted much interest as a new class of thermoelectric materials.\footnote{B.C. Sales, D. Mandrus, and R. K. Williams, Science \textbf{272}, 1325 (1996).} We have determined the electronic structures, optical and thermoelectric propertes of Tl-filled skutterudite CoSb$_3$ by using the highly precise full-potential linearized augmented plane wave (FLAPW) method\footnote{Wimmer, Weinert, Krakauer, Freeman, Phys. Rev. B \textbf{24}, 864 (1981).} within the Perdew-Burke-Ernzerhof (PBE)\footnote{Perdew, Burke, Ernzerhof, Phys. Rev. Lett. \textbf{77}, 3865 (1996).} form of the generalized gradient approximation (GGA) to density functional theory. In contrast to the small-gap semiconducting CoSb$_3$, Tl-filled CoSb$_3$ is calculated to be metallic with Tl-$sp$ bands stongly hybridized with all the other elements over the entire energy region. The thermoelectric properties, \textit{e.g.} the Seebeck coefficient, are evaluated and discussed in terms of the diagonal terms of the optical matrix elements.