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• For the first time, first-principles calculations are used to predict the lattice thermal conductivity of free-standing monolayer XS2 (X = mo and W) and monolayer XS2 supported on SiC (0001) and ZnO (0001) substrates. • The lattice thermal conductivity of monolayer XS2 supported on SiC (0001) and ZnO (0001) substrates show a significant decrease, and the decrease is even greater for the monolayer XS2 supported on ZnO (0001) substrates, reaching about 65–70 %. • The substrate drives softening of the acoustic branch, making the low-frequency phonon group velocity decrease and the three-phonon scattering enhance. • From the perspective of atomic bonding, the substrate breaks the symmetry of bonding of monolayer XS2, which leads to the increase of phonon anharmonicity and ultimately to a decrease in thermal conductivity of monolayer XS2. Thermoelectric materials have properties such as direct conversion of waste heat into electricity and environmental friendliness, which make them promising for renewable energy utilization, however, the lower conversion efficiency limits the large-scale application of thermoelectric materials. Monolayer transition metal dichalcogenides (TMDs) are candidates for thermoelectric materials due to their high power factor, but their higher thermal conductivity (TC) limits the further improvement of the figure of merit (ZT). Here, we employ first-principles calculations and solve the Boltzmann transport equation (BTE) to compare the lattice TC of free-standing monolayer XS 2 (X = Mo and W) and monolayer XS 2 supported on SiC (0001) and ZnO (0001) substrates. We find that the lattice TC of monolayer XS 2 supported on SiC (0001) and ZnO (0001) substrates are sharply reduced. Especially supported on the ZnO (0001) substrate, the lattice TC of XS 2 reduce by 65 %–70 %, which is expected to improve the thermoelectric properties of monolayer XS 2. In addition, we report the underlying cause of this significant reduction in TC. Firstly, the substrate drives softening of the acoustic branch, which leads to a decrease of phonon group velocity in the low-frequency and an enhancement of the three-phonon scattering. Then, the asymmetric bonding of XS 2 is induced by the substrates, which enhance phonon anharmonicity and reduce the phonon lifetime. Our results demonstrate that the lattice TC of monolayer XS 2 can be tuned by adjusting the substrate, which has certain reference values for the thermoelectric design of XS 2. SiC (0001) and ZnO (0001) substrates break the symmetry of the monolayer XS 2 (X = Mo and W) bonding, resulting in an increase in phonon anharmonicity, which reduces the contribution of the low-frequency acoustic branch of monolayer XS 2 to the thermal conductivity. [Display omitted] [ABSTRACT FROM AUTHOR]