Thermal conductivity and phonon hydrodynamics in transition metal dichalcogenides from first-principles

We carry out a systematic study of the thermal conductivity of four single-layer transition metal dichalcogenides, MX$_2$ (M = Mo, W; X = S, Se) from first-principles by solving the Boltzmann Transport Equation (BTE). We compare three different theoretical frameworks to solve the BTE beyond the Relaxation Time Approximation (RTA), using the same set of interatomic force constants computed within density functional theory (DFT), finding that the RTA severely underpredicts the thermal conductivity of MS$_2$ materials. Calculations of the different phonon scattering relaxation times of the main collision mechanisms and their corresponding mean free paths (MFP) allow evaluating the expected hydrodynamic behaviour in the heat transport of such monolayers. These calculations indicate that despite of their low thermal conductivity, the present TMDs can exhibit large hydrodynamic effects, being comparable to those of graphene, especially for WSe$_2$ at high temperatures.