Exceptional thermoelectric properties in Na$_2$TlSb enabled by quasi-1D band structure

Materials with reduced dimensionality offer beneficial density-of-states (DOS) profiles for thermoelectric energy conversion, but can be impractical in realistic devices. Encouragingly, bulk high-symmetry materials can also exhibit similar quasi-low-dimensional band structures. A striking example is the full-Heusler compound Na$_2$TlSb, whose valence-band energy isosurfaces can form intersecting two-dimensional pockets, i.e., a box-like structure. The individual energy isosurface sheets resemble those of 1D quantum wires. The combination of high electron velocities (perpendicular to the pockets) and a rapidly increasing DOS with energy in the transport regime (due to the low dimensionality) makes Na$_2$TlSb a representative case where the band structure gives rise to attractive electronic transport properties. However, these beneficial features could be counteracted by high electronic scattering rates due to the large scattering space. In this first principles study of Na$_2$TlSb we find that the electronic scattering rates remain modest. This result is linked to the reduced matrix elements of large-momentum ($\mathbf{q}$) scattering across the delocalized energy isosurfaces. The enhanced free-carrier screening due to the large DOS also contributes to reducing scattering. In combination, the low-dimensional features and modest scattering result in excellent electronic transport properties. Combined with an ultra-low lattice thermal conductivity of $\kappa_\ell < 1$ W/mK reported in the literature, we predict a thermoelectric figure of merit ranging from 2.4 at 300 K to a 4.4 at 600 K. The $n$-type properties are also favorable, with $zT$ values from 1.5 at 300 K to 3.0 at 600 K.