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The manipulation of two-dimensional materials via their dielectricenvironment offers novel opportunities to control electronic as well as opticalproperties and allows to imprint nanostructures in a non-invasive way. Here weasses the potential of monolayer semiconducting transition metaldichalcogenides (TMDCs) for Coulomb engineering in a material realistic andquantitative manner. We compare the response of different TMDC materials tomodifications of their dielectric surrounding, analyze effects of dynamicsubstrate screening, i.e. frequency dependencies in the dielectric functions,and discuss inherent length scales of Coulomb-engineered heterojunctions. Wefind symmetric and rigid-shift-like quasi-particle band-gap modulations forboth, instantaneous and dynamic substrate screening. From this we deriveshort-ranged self energies for an effective multi-scale modeling of Coulombengineered heterojunctions composed of an homogeneous monolayer placed on aspatially structured substrate. For these heterojunctions, we show that bandgap modulations on the length scale of a few lattice constants are possiblerendering external limitations of the substrate structuring more important thaninternal effects. We find that all semiconducting TMDCs are similarly wellsuited for these external and non-invasive modifications.

Coulomb-Engineered Heterojunctions and Dynamical Screening in Transition Metal Dichalcogenide Monolayers