Thermoelectric transport properties of PbTe under pressure

Abstract

In this work, we present a comprehensive picture of structural, dynamical, electronic, and transport properties of PbTe at ambient and high pressures. The first-principles linear-response calculations show that there exists an anharmonic instability of the optical branch phonon at the Brillouin-zone (BZ) center and soft phonons at the BZ boundary X point. The $\mathbit{k}$-dependent soft modes may lead to substantial changes in the thermal conductivity when the pressure is applied. The electronic band structure of both $B1$ and $Pnma$ phases are investigated by full potential method with various exchange-correlation functionals. Under pressure there is a band-gap closure as well as reopening within $B1$ structure whereas for $Pnma$ phase only the gap closure is observed. Their thermoelectric transport properties are studied by exploring their energy bands based on Boltzmann transport theory. We found that $n$-doped $Pnma$ phase at 6.7 GPa has better thermoelectric performance than $B1$ phase at ambient condition, while for the $p$-doped case, $B1$ phase has much better thermoelectric properties. Energy band gap does play an important role in thermoelectric performance. At 300 K, modifications of thermoelectric properties caused by band-gap variation can be observed only at a low doping level, at 600 K the influence can be detected in mid-to-high doping levels. The detailed analysis of thermoelectric properties as respect to temperatures and carrier concentrations reveal that in the low-doping case the optimal performance occurs in 300--450 K temperature range but for mid-to-high doping cases the optimal working temperature increase to higher range. With the pressure applied, the thermoelectric response shows many interesting features. The thermoelectric figure of merit $(ZT)$ for $B1$ phase achieves its maximum at middoping region with $\ensuremath{\sim}8\text{ }\text{GPa}$ for $p$ doping and above 18 GPa for $n$ doping. In the $Pnma$ case, $ZT$ values are more sensitive to doping than to pressure, and there is small difference between the 300 and 600 K results. These findings are expected to be useful in searching an optimal combination of doping level, working temperature, and pressure in order to achieve higher $ZT$ in PbTe-based materials.