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We compute the electronic structure of two-dimensional (2D) materialsdecorated with self-assembled organic monolayers using density functionaltheory. We find that 2D materials are strongly impacted by near-fieldelectrostatic effects resulting from high multipoles of the organic layerelectronic density. We show that this effect can lead to significant (~0.5V)modulation of the in-plane potential experienced by electrons in 2D materialswithin ~4\AA from the molecular layer, with a transition between near- andfar-field depending on the lateral extent of the molecules. We develop a theoryof this effect, showing that the electrostatic potential of the molecular layercan be approximated by a discretized planar charge density derived from themolecular structure and multipoles. Solving this model computationally andanalytically, we propose implementations of this effect to generate novelelectronic properties for electrons in 2D materials, such as band gap openingand anisotropic group velocity modulation for monolayer graphene fromexperimentally achievable molecular assemblies.

Engineering the Electronic Structure of Two-Dimensional Materials with Near-Field Electrostatic Effects of Self-Assembled Organic Layers