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

Abstract

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 $κ_\ell < 1$ 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.

Figures (10)

• Figure 1: Energy isosurfaces of the Na$_2$TlSb valence band obtained with density functional theory. Just below the band edge (a), the valence band forms 12 Fermi pockets between $\Gamma$ and K, but these merge into continuous box-like isosurfaces shown at 0.12 eV below the VBM in (b). The box surfaces consist of pairs of sheets giving a hollow energy isosurface. Moving to 0.30 eV below the VBM, the isosurface expands to six overlapping sheets, shown from two different perspectives in (c) and (d). The color gradient indicates the $y$-component of the electron group velocity, highlighting how the sheets contribute individually to transport in the direction perpendicular to the sheets.
• Figure 2: (a) Atom-projected electronic band structure and (b) the orbital and total electronic DOS of Na$_2$TlSb calculated with the HSE06 functional and spin-orbit coupling.
• Figure 3: Effective (a) and cumulative (b) normalized transport contributions at different energies, with Fermi selection functions $W^{(\alpha)}$ in Eq. \ref{['eq: self_func']} based on the Fermi level optimizing $zT$ (red vertical line) at 600 K. The vertical black lines correspond, respectively, to the energy isosurfaces of Fig. \ref{['fig: fermi']}.
• Figure 4: The Seebeck coefficient ($S$), mobility ($\mu$), electrical conductivity ($\sigma$), electron thermal conductivity ($\kappa_\mathrm{e}$), power factor (PF), and figure of merit ($zT$) of p-type Na$_2$TlSb at temperatures 200--700 K.
• Figure 5: $zT$ as a function of temperature for various carrier concentrations for (a) p- and (b) n-type doping. The highest achievable average $zT$ over the range 300--700 K is also indicated.