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Screening for Two dimensional MX$_2$ semiconductors with possible high room temperature mobility

We calculated the electron mobility of 14 two dimensional semiconductors with composition of MX$_2$, where M (= Mo, W, Sn, Hf, Zr and Pt) is the transition metal, and X is S, Se and Te. We treated the scattering matrix by deformation potential approximation. Long wave longitudinal acoustical and optical phonon scatterings are included. Piezoelectric scattering in the compounds without inversion symmetry is also taken into account. We found that out of the 14 compounds, WSe$_2$, PtS$_2$ and PtSe$_2$, are promising regarding to the possible high electron mobility and finite band gap. The phonon limited mobility in PtSe$_2$ reaches about 3000 cm$^2$V$^{-1}$s$^{-1}$ at room temperature which is the highest among the compounds. The bandgap under the local density approximation is 1.25 eV. Our results can be a guide for experiments to search for better two-dimensional materials for future semiconductor devices.