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 HfS 2 (2.19 W m −1 K −1 ), HfSe 2 (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, Bi 2 Te 3 (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 MoS 2 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 7.4 e on the Hf ions, which is seven times that on Mo in MoS 2 single layer. Enhancement in k L occurs in HfS 2 (2.19 to 4.1 W m −1 K −1 ), HfSe 2 (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 MoS 2 . 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.