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