  Two-dimensional transition metal dichalcogenides (TMDCs) are finding
promising electronic and optical applications due to their unique properties.
In this letter, we systematically study the phonon transport and thermal
conductivity of eight semiconducting single-layer TMDCs, MX2 (M=Mo, W, Zr and
Hf, X=S and Se), by using the first-principles-driven phonon Boltzmann
transport equation approach. The validity of the single-mode relaxation time
approximation to predict the thermal conductivity of TMDCs is assessed by
comparing the results with the iterative solution of the phonon Boltzmann
transport equation. We find that the phononic thermal conductivities of 2H-type
TMDCs are above 50 W/mK at room temperature while the thermal conductivity
values of the 1T-type TMDCs are much lower, when the size of the sample is 1
{\mu}m. A very high thermal conductivity value of 142 W/mK was found in
single-layer WS2. The large atomic weight difference between W and S leads to a
very large phonon bandgap which in turn forbids the scattering between acoustic
and optical phonon modes and thus resulting in very long phonon relaxation
time.
