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

We develop an ab initio formalism for dipolar electron-phonon interactions (EPI) in two-dimensional (2D) materials. Unlike purely longitudinal Fr\"ohlich model, we show that the out-of-plane dipoles also contribute, and the 2D dipolar EPI plays an important role not only in the typical polar material MoS$_2$, but also in hydrocarbon material graphane. 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 Fr\"ohlich model is inadequate for 2D materials and correct long-wavelength interaction must be included for the reliable prediction.