Thermoelectric transport of strained CsK$_2$Sb: The role of electron velocities and scattering within extended Fermi surfaces

Abstract: In this first-principles study, we investigated the thermoelectric properties of the full-Heusler compound CsK$_2$Sb at different compressive strains. This material exhibits a valence band structure with significant effective mass anisotropy, forming tube-like energy isosurfaces below the band edge, akin to that of two-dimensional (2D) systems. Such systems can have a large number of high-mobility charge carriers and a beneficial density of states profile. In the calculations, we predicted a maximum p-type figure of merit ($zT$) of 2.6 at 800 K, in line with previous predictions of high $zT$. This high $zT$ arises from the low lattice thermal conductivity of 0.35 Wm$^{-1}$K$^{-1}$ and the beneficial electronic band structure. The high density of states significantly increased the electron-scattering space, but this effect was largely compensated by reduced scattering rates of electrons with large momentum ${\mathbf{q}}$. We further explored the effect of enhancing the low-dimensionality through compressive strain. This increased the p-type power factor by up to 66 %; partly due to more strongly pronounced 2D features of the valence band, but primarily due to increased Fermi velocities. However, compressive strain also increased phonon velocities and hence the lattice thermal conductivity. The maximum p-type $zT$ thus only increased slightly, to 2.7 at 1 % compressive strain. In the conduction band, strain aligned the $\Gamma$- and X-centered valleys, resulting in the optimal n-type $zT$ increasing from 0.9 to 2.3 at 2 % compressive strain. Thus, highly strained CsK$_2$Sb has the potential for both good p- and n-type thermoelectricity.