Remarkable thermoelectric performance in ${\mathrm{BaPdS}}_2$ via pudding-mold band structure, band convergence, and ultralow lattice thermal conductivity

Efficient thermoelectric materials require a rare and contraindicated combination of materials properties: large electrical conductivity, large Seebeck coefficient, and low thermal conductivity. One strategy to achieve the first two properties is via low-energy electronic bands containing both flat and dispersive parts in different regions of crystal momentum space, known as a pudding-mold band structure. Here, we illustrate that ${\mathrm{BaPdS}}_2$ successfully achieves the pudding-mold band structure for the valence band, contributing to a large $p$-type thermoelectric power factor, due to its anisotropic crystal structure containing zigzag chains of edge-sharing square planar ${\mathrm{PdS}}_4$ units; large power factor is achieved for $n$-type doping as well due to band convergence. In addition, ${\mathrm{BaPdS}}_2$ exhibits ultralow lattice thermal conductivity, and thus also achieves the third property, due to extremely soft and anharmonic interactions in its transverse acoustic phonon branch. We predict a remarkably large thermoelectric figure of merit, with peak values between 2 and 3 for two of the three crystallographic directions, suggesting ${\mathrm{BaPdS}}_2$ warrants experimental investigation.

Figure 1

Orthographic projection of the crystal structure of ${\mathrm{BaPdS}}_2$ along the (a) c and (b) a axes of the conventional unit cell (red dashed lines). The green, gray, and yellow circles represent Ba, Pd, and S atoms, respectively. Black lines indicate the Pd-S bonds of the square planar units. (c) The electronic bands of ${\mathrm{BaPdS}}_2$ colored by the Pd $d$ character of the electronic states. The zero of energy is set to the valence band maximum, and the black horizontal dotted lines indicate the $\pm {10}^{20}{\mathrm{cm}}^{-3}$ doping levels.

Figure 2

(a) Power factor divided by electronic relaxation time as a function of carrier concentration for ${\mathrm{BaPdS}}_2$ (lines) and SnSe (circles), averaged over the $x, y$, and $z$ directions, for several values of $T$. (b) $T=700$ K power factor divided by electronic relaxation time versus carrier concentration in each direction, in addition to the average, for ${\mathrm{BaPdS}}_2$.

Figure 3

(a) ${\mathrm{BaPdS}}_2$ phonon bands colored by Ba contribution to the phonon eigenvector. (b) The low-frequency portion of the phonon dispersion with bands colored by the magnitude of the mode Grüneisen parameter. (c) Dispersion of the mode Grüneisen parameter ${\gamma }_{\mathbf{q}\nu }$ for the acoustic branches. Due to the large ${\gamma }_{\mathbf{q}\nu }$ values for the TA branch along $\mathrm{\Gamma }$-X, we use a broken ${\gamma }_{\mathbf{q}\nu }$ axis for clarity.

Figure 4

(a)–(c) Stacked plots of ${\mathrm{BaPdS}}_2$ acoustic branch contributions to ${\kappa }_L$ versus $T$ computed via the Debye-Callaway model for the (a) $x$, (b) $y$, and (c) $z$ directions, respectively. Red lines indicate the minimum ${\kappa }_L$ of the Cahill model. (d)–(f) $ZT$ as a function of carrier concentration for different $T$ in the (d) $x$, (e) $y$, and (f) $z$ directions, respectively. Values are shown for $\tau =5$ fs.