Lattice vibrational modes and phonon thermal conductivity of monolayer MoS2

The anharmonic behavior of phonons and intrinsic thermal conductivity associated with the umklapp scattering in monolayer MoS${}_{2}$ sheet are investigated via first-principles calculations within the framework of density functional perturbation theory. In contrast to the negative Gr\"uneissen parameter ($\ensuremath{\gamma}$) occurring in low-frequency modes in graphene, positive $\ensuremath{\gamma}$ in the whole Brillouin zone is demonstrated in monolayer MoS${}_{2}$ with much larger $\ensuremath{\gamma}$ for acoustic modes than that for the optical modes, suggesting that monolayer MoS${}_{2}$ sheet possesses a positive coefficient of thermal expansion. The calculated phonon lifetimes of the infrared active modes are 5.50 and 5.72 ps for ${E}^{\ensuremath{'}}$ and ${A}_{2}^{\ensuremath{'}\ensuremath{'}}$, respectively, in good agreement with experimental results obtained by fitting the dielectric oscillators with the infrared reflectivity spectrum. The lifetime of the Raman ${A}_{1}^{\ensuremath{'}}$ mode (38.36 ps) is about seven times longer than those of the infrared modes. The dominated phonon mean free path of monolayer MoS${}_{2}$ is less than 20 nm, about 30-fold smaller than that of graphene. Combined with the nonequilibrium Green's function calculations, the room temperature thermal conductivity of monolayer MoS${}_{2}$ is found to be around 23.2 W m${}^{\ensuremath{-}1}$ K${}^{\ensuremath{-}1}$, two orders of magnitude lower than that of graphene.