Ternary transition-metal nitride halide monolayers MNI (M = Zr, Hf) with low thermal conductivity and high thermoelectric figure of merit

Machine learning-based approaches are promising in pursuing the thermal properties of two-dimensional materials. Here, a comprehensive study of thermal transport and thermoelectric properties of the $\beta$-form of ZrNI and HfNI monolayers, a family of ternary transition-metal nitride halides (TMNH), is presented by employing machine learning-based interatomic potential, Boltzmann transport theory, and first-principles calculations. The monolayer isolation and its stability are confirmed via cleavage energies, phonon dispersions, and ab initio molecular dynamics simulations. At room temperature, the lattice thermal conductivity of the ZrNI and HfNI monolayers are 7.8 W/(m$\cdot$K) and 11.7 W/(m$\cdot$K), respectively, which are considerably lower than those of typical 2D materials. The power factor of n-type doped ZrNI layer is 9 times higher than the HfNI monolayer due to high electrical conductivity of ZrNI. Also, the maximum figure of merit values of the n-type ZrNI always appears higher than the HfNI monolayer regardless of temperature. However, both the ZrNI and HfNI layers show superior thermoelectric properties over typical 2D materials. It reveals that the n-type ZrNI monolayer is a beneficial material for thermoelectric applications.