Long-range electrostatic contribution to the electron-phonon couplings and mobilities of two-dimensional and bulk materials

Charge transport plays a crucial role in manifold potential applications of two-dimensional materials, including field effect transistors, solar cells, and transparent conductors. At most operating temperatures, charge transport is hindered by scattering of carriers by lattice vibrations. Assessing the intrinsic phonon-limited carrier mobility is thus of paramount importance to identify promising candidates for next-generation devices. Here we provide a framework to efficiently compute the drift and Hall carrier mobility of two-dimensional materials through the Boltzmann transport equation by relying on a Fourier-Wannier interpolation. Building on a recent formulation of long-range contributions to dynamical matrices and phonon dispersions [Phys. Rev. X 11, 041027 (2021)], we extend the approach to electron-phonon coupling including the effect of dynamical dipoles and quadrupoles. We identify an unprecedented contribution associated with the Berry connection that is crucial to preserve the Wannier-gauge covariance of the theory. This contribution is not specific to 2D crystals, but also concerns the 3D case, as we demonstrate via an application to bulk SrO. We showcase our method on a wide selection of relevant monolayers ranging from SnS₂ to MoS₂, graphene, BN, InSe, and phosphorene. We also discover a non-trivial temperature evolution of the Hall hole mobility in InSe whereby the mobility increases with temperature above 150~K due to the mexican-hat electronic structure of the InSe valence bands. Overall, we find that dynamical quadrupoles are essential and can impact the carrier mobility in excess of 75%.