Ultra-low lattice thermal conductivity and giant phonon–electric field coupling in hafnium dichalcogenide monolayers

Phonons in crystalline solids are of utmost importance in governing its lattice thermal conductivity (k L). In this work, k L in hafnium (Hf) dichalcogenide monolayers has been investigated based on ab initio DFT coupled to linearized Boltzmann transport equation together with single-mode relaxation-time approximation. Ultra-low k L found in HfS2 (2.19 W m-1 K-1), HfSe2 (1.23 W m-1 K-1) and HfSSe (1.78 W m-1 K-1) monolayers at 300 K, is comparable to that of the state-of-art bulk thermoelectric materials, such as, Bi2Te3 (1.6 W m-1 K-1), PbTe (2.2 W m-1 K-1) and SnSe (2.6 W m-1 K-1). Gigantic longitudinal-transverse optical (LO-TO) splitting of up to 147.7 cm-1 is noticed at the Brillouin zone-centre (Γ-point), which is much higher than that in MoS2 single layer (∼2 cm-1). It is driven by the colossal phonon-electric field coupling arising from the domination of ionic character in the interatomic bonds and Born effective or dynamical charges as high as 7.4e on the Hf ions, which is seven times that on Mo in MoS2 single layer. Enhancement in k L occurs in HfS2 (2.19 to 4.1 W m-1 K-1), HfSe2 (1.23 to 1.7 W m-1 K-1) and HfSSe (1.78 to 2.2 W m-1 K-1) upon the incorporation of the non-analytic correction term. Furthermore, the mode Grüneisen parameter is calculated to be as high as ∼2.0, at room temperature, indicating a strong anharmonicity. Moreover, the contribution of optical phonons to k L is found to be ∼12%, which is significantly high than that in single-layer MoS2. Large atomic mass of Hf (178.5 u), small phonon group velocities (4-5 km s-1), low Debye temperature (∼166 K), low bond and elastic stiffness (Young's modulus ∼75 N m-1), small phonon lifetimes (∼6 ps), low specific heat capacity (∼17 J K-1 mol-1) and strong anharmonicity are collectively found to be the factors responsible for such a low k L. These findings would be immensely helpful in designing thermoelectric interconnects at the nanoscale and 2D material-based energy harvesters.