  Improving the figure of merit $zT$ of thermoelectric materials requires
simultaneously a high power factor and low thermal conductivity. An effective
approach for increasing the power factor is to align the band extremum and
achieve high band degeneracy ($\geq$ 12) near the Fermi level as realized in
PbTe [\textcolor{blue}{Pei et. al. \textit{Nature} 473, 66 (2010)}], which
usually relies on band structure engineering, e.g., chemical doping and strain.
However, very few materials could achieve such a high band degeneracy without
heavy doping or suffering impractical strain. By employing state-of-the-art
first-principles methods with direct computation of phonon and carrier
lifetime, we demonstrate that two new full-Heusler compounds Li$_2$TlBi and
Li$_2$InBi, possessing a PbTe-like electronic structure, show exceptionally
high power factors ($\sim$ 20 mWm$^{-1}$K$^{-2}$ at 300 K) and low lattice
thermal conductivities (2.36 and 1.55 Wm$^{-1}$K$^{-1}$) at room temperature.
The Tl$^{+}$Bi$^{3-}$ (In$^{+}$Bi$^{3-}$) sublattice forms a rock-salt
structure, and the additional two valence electrons from Li atoms essentially
make these compounds isovalent with Pb$^{2+}$Te$^{2-}$. The larger rock-salt
sublattice of TlBi (InBi) shifts the valence band maximum from L point to the
middle of the $\Sigma$ line, increasing the band degeneracy from fourfold to
twelvefold. On the other hand, resonance bond in the PbTe-like sublattice and
soft Tl-Bi (In-Bi) bonding interaction is responsible for intrinsic low lattice
thermal conductivities. Our results present a novel strategy of designing
high-performance thermoelectric materials.
