Ultralow lattice thermal conductivity induced by anharmonic cation rattling and significant role of intrinsic point defects in TlBiS2

Understanding the nature of chemical bonding and lattice dynamics, and their impacts on phonon transport, is crucial for exploring and designing thermoelectric materials with ultralow lattice thermal conductivity. Hexagonal ${\mathrm{TlBiS}}_{2}$ exhibits a low lattice thermal conductivity ${\ensuremath{\kappa}}_{l}$ of 0.67 W/mK at room temperature. The low lattice thermal conductivity is attributed to anharmonic rattling vibration of the weakly bound Tl cations as well as anharmonic motion of the Bi. The soft anharmonic motions of Tl and Bi arise due to the unique electronic structure of this material, which includes substantial cross-gap hybridization involving Tl, Bi, and S. This characteristic leads to a very high dielectric constant, which is favorable for high mobility in the presence of point defects. Different from the long-standing view that acoustic phonons with long mean-free paths invariably are the primary heat carriers contributing to ${\ensuremath{\kappa}}_{l}$, we show that 59% of ${\ensuremath{\kappa}}_{l}$ of ${\mathrm{TlBiS}}_{2}$ is contributed by optical phonons. We explicitly analyze the mechanism by which optical phonons in ${\mathrm{TlBiS}}_{2}$ contribute to heat transport. These optical phonons have large Gr\"uneisen parameters and high anharmonic scattering rate, but in ${\mathrm{TlBiS}}_{2}$ they also have high group velocities, resulting in significant contributions in this low thermal conductivity material. We find that intrinsic point defects can be utilized to improve the thermoelectric properties of ${\mathrm{TlBiS}}_{2}$. The Tl vacancy is found to be the dominant defect and can be introduced to improve the band degeneracy and transport properties. Calculations demonstrate that ${\mathrm{V}}_{\mathrm{Tl}}$ is a shallow acceptor. Adjusting the Fermi level using Tl vacancies to increase the carrier concentration of $p$-type ${\mathrm{TlBiS}}_{2}$ is one important strategy to improve its thermoelectric performance. Our paper provides one method for studying and exploring applications with ultralow lattice thermal conductivity and improving thermoelectric properties using intrinsic point defects.