Title: Guidelines for accurate and efficient calculations of mobilities in two-dimensional materials

Abstract: Emerging two-dimensional (2D) materials bring unprecedented opportunities for electronic applications. The design of high-performance devices requires an accurate prediction of carrier mobility in 2D materials, which can be obtained using state-of-the-art $ab~initio$ calculations. However, various factors impact the computational accuracy, leading to contradictory estimations for the mobility. In this work, targeting accurate and efficient $ab~initio$ calculations, transport properties in III-V monolayers are reported using the Boltzmann transport equation, and the influences of pseudopotential, quadrupole correction, Berry connection, and spin-orbit coupling (SOC) on mobilities are systematically investigated. Our findings are as follows: (1) The inclusion of semi-core states in pseudopotentials is important to obtain accurate calculations. (2) The variations induced by dynamical quadrupole and Berry connection when treating long range fields can be respectively 40% and 10%. (3) The impact of SOC can reach up to 100% for materials with multi-peak bands. Importantly, although SOC notably modifies the electronic wavefunctions, it negligibly impacts the dynamical matrices and scattering potential variations. As a result, the combination of fully-relativistic electron calculation and scalar-relativistic phonon calculation can strike a good balance between accuracy and cost. This work compares computational methodologies, providing guidelines for accurate and efficient calculations of mobilities in 2D semiconductors.