Analytical Theory of Near-Field Electrostatic Effects in Two-Dimensional Materials and van der Waals Heterojunctions

We derive and validate a quantitative analytical model of the near-field electrostatic effects in the vicinity (>=3\AA) of two-dimensional (2D) materials. In solving the Poisson equation of a near-planar point charge ansatz for the electronic density of a 2D material, our formula quantitatively captures the out-of-plane decay and the in-plane modulation of density functional theory (DFT)-calculated potentials. We provide a method for quickly constructing the electronic density ansatz, and apply it to the case of hexagonal monolayers (BN, AlN, GaN) and monochalcogenides (GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, PbTe) and their flexural and polar distortions. We demonstrate how our model can be straightforwardly applied to predict material-/angle-specific moir\'e potentials arising in twisted superlattices with periodicities beyond the reach of DFT calculations.