Colossal Thermoelectric Power Factor in K$_{7/8}$RhO$_2$

We discuss the thermoelectric and optical properties of layered K$_{x}$RhO$_{2}$ (\emph{x} = 1/2 and 7/8) in terms of the electronic structure determined by first principles calculations as well as Boltzmann transport theory. Our optimized lattice constants differ significantly from the experiment, but result in optical and transport properties close to the experiment. The main contribution to the optical spectra are due to intra and inter-band transitions between the Rh 4\emph{d} and O 2\emph{p} states. We find a similar power factor for pristine K$_{x}$RhO$_{2}$ at low and high cation concentartions. Our transport results of hydrated K$_{x}$RhO$_{2}$ at room temperature show highest value of the power factor among the hole-type materials. Specially at 100 K, we obtain a value of 3$\times$10$^{-3}$ K$^{-1}$ for K$_{7/8}$RhO$_{2}$, which is larger than that of Na$_{0.88}$CoO$_{2}$ {[}M. Lee \emph{et al}., Nat. Mater. 5, 537 (2006){]}. In general, the electronic and optical properties of K$_{x}$RhO$_{2}$ are similar to Na$_{x}$CoO$_{2}$ with enhanced transport properties in the hydrated phase.