  Two-dimensional (2D) semiconductors have demonstrated great potential for
next-generation electronics and optoelectronics. An important property for
these applications is the phonon-limited charge carrier mobility. The common
approach to calculate the mobility from first principles relies on the
interpolation of the electron-phonon coupling (EPC) matrix. However, it
neglects the scattering by the dynamical quadrupoles generated by phonons,
limiting its accuracy. Here we present a first-principles method to incorporate
the quadrupole scattering, which results in a much better interpolation quality
and thus a more accurate mobility as exemplified by monolayer MoS2 and InSe.
This method also allows for a natural incorporation of the effects of the free
carriers, enabling us to efficiently compute the screened EPC and thus the
mobility for doped semiconductors. Particularly, we find that the electron
mobility of InSe is more sensitive to the carrier concentration than that of
MoS2 due to the stronger long-range scattering in intrinsic InSe. With
increasing electron concentration, the InSe mobility can reach ~4 times of the
intrinsic value, then decrease owing to the involvement of heavier electronic
states. Our work provides accurate and efficient methods to calculate the
phonon-limited mobility in the intrinsic and doped 2D materials, and improves
the fundamental understanding of their transport mechanism.
