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Over the last few years, $ab~initio$ methods have become an increasinglypopular tool to evaluate intrinsic carrier transport properties in 2Dmaterials. The lack of experimental information, and the progress made in thedevelopment of DFT tools to evaluate electronic band structures, phonondispersions, and electron-phonon scattering matrix-elements, have made them afavored choice. However, a large discrepancy is observed in the literatureamong the $ab~initio$ calculated carrier mobility in 2D materials. Some of thediscrepancies are a result of the physical approximations made in calculatingthe electron-phonon coupling constants and the carrier mobility. Theseapproximations can be avoided by using a sophisticated transport model.However, despite using appropriate transport models, the uncertainty in thereported carrier mobility is still quite large in some materials. The majordifferences observed between these refined model calculations are the `flavors'of DFT (exchange-correlation functional, pseudopotential, and the effect ofspin-orbit coupling) used. Here, considering several monolayer 2H-TMDs asexamples, we calculate the low- and high-field transport properties usingdifferent `flavors' of DFT, and calculate a range for the electron mobilityvalues. We observe that in some materials the values differ by orders ofmagnitude (For example, in monolayer WS$_{2}$ the electron low-field mobilityvaries between 37 cm$^{2}$/(V$\cdot$s) and 767 cm$^{2}$/(V$\cdot$s)). Weanalyze critically these discrepancies, and try to understand the limitationsof the current $ab~initio$ methods in calculating carrier transport properties.

Limitations of ab initio methods to predict the electronic-transport  properties of two-dimensional materials: The computational example of  2H-phase transition metal dichalcogenides