Theory of near-field electrostatic effects in van der Waals heterostructures and Moiré structures*

Recent advances in the fabrication and characterization of van der Waals heterostructures have demonstrated large tunability of their optoelectronic properties with respect to the relative twist and sliding of the structures. Beyond the quantum mechanical coupling between adjacent layers, 2D materials can impact the local electrostatic potential. At typical 2D-2D materials distance, near-field effects can be dominant and a multipole expansion of the potential become insufficient to capture the materials descriptors.

In this work, we develop a theory of the near-field electrostatic effects of 2D materials. We show using density functional theory that the electrostatic potential of a vast number of 2D materials is well approximated by a discretized charge density model. We derive simple analytical expressions of the electrostatic potential V(x,y,z), and show their applicability to the case of van der Waals and Moiré structures.