Ab initio dipolar electron-phonon interactions in two-dimensional materials

We develop an ab initio formalism for dipolar electron-phonon interactions (EPIs) in two-dimensional (2D) materials. Unlike the purely longitudinal Fr\"ohlich model, we show that the out-of-plane dipoles also contribute to the long-wavelength nonanalytical behavior of EPIs. And the 2D dipolar EPI plays an important role not only in the typical polar material ${\text{MoS}}_{2}$, but also in graphane and fluorinated graphene. By incorporating this formalism into Wannier-Fourier interpolation, we enable accurate EPI calculations for 2D materials and subsequent intrinsic carrier mobility prediction. The results show that the Fr\"ohlich model is inadequate for 2D materials and a correct long-wavelength interaction must be included for a reliable prediction.