High $n$-type thermoelectric power factor and efficiency in Ba$_{2}$BiAu from a highly dispersive band

Using first-principles density-functional theory calculations, we predict the potential for unprecedented thermoelectric efficiency $zT=5$ at 800 K in $n$-type Ba$_{2}$BiAu full-Heusler compound. Such a high efficiency arises from an intrinsically ultralow lattice thermal conductivity coupled with a very high power factor reaching 7 mW m$^{-1}$ K$^{-2}$ at 500 K. The high power factor originates from a light, sixfold degenerate conduction band pocket along the $Gamma$-X direction. Weak acoustic phonon scattering and sixfold multiplicity combine to yield high mobility and high Seebeck coefficient. In contrast, the flat-and-dispersive (a.k.a. low-dimensional) valence band of Ba$_{2}$BiAu fail to generate a high power factor due to strong acoustic phonon scattering. The Lorenz numbers at optimal doping are smaller than the Wiedemann-Franz value, an integral feature for $zT$ enhancement as electrons are the majority heat carriers.