We propose to create lateral heterojunctions in two-dimensional materials based on nonlocal manipulations of the Coulomb interaction using structured dielectric environments. By means of ab initio calculations for MoS2 as well as generic semiconductor models, we show that the Coulomb interaction-induced self-energy corrections in real space are sufficiently nonlocal to be manipulated externally, but still local enough to induce spatially sharp interfaces within a single homogeneous monolayer to form heterojunctions. We find a type-II heterojunction band scheme promoted by a laterally structured dielectric environment, which exhibits a sharp band gap crossover within less than 5 unit cells.

We investigate the effects of environmental dielectric screening on the electronic dispersion and the band gap in the atomically-thin, quasi two-dimensional (2D) semiconductor WS2 using correlative angle-resolved photoemission and optical spectroscopies, along with first-principles calculations. We find the main effect of increased environmental screening to be a reduction of the band gap, with little change to the electronic dispersion of the band structure. These essentially rigid shifts of the bands results from the special spatial structure of the changes in the Coulomb potential induced by the dielectric environment in the 2D limit. Our results suggest dielectric engineering as a noninvasive method of tailoring the band structure of 2D semiconductors and provide guidance for understanding the electronic properties of 2D materials embedded in multilayer heterostructures.In monolayers of atomically-thin, quasi twodimensional (2D) semiconductors, the intrinsic screening of Coulomb interactions is reduced compared to their bulk crystals, since electric field lines between charges extend significantly outside the material. As a result, exciton binding energies are enhanced, reaching values of several hundreds of meV in the transition metal dichalcogenides (TMDCs) [1][2][3][4][5][6][7]. For the same reason, materials in close proximity to the monolayers enhance the effective screening of charge carrier interactions. By embedding atomically-thin materials in different dielectric environments, their band gaps, as well as exciton binding energies, can therefore be modified on an energy scale of the exciton binding energies themselves [8][9][10]. This sensitivity becomes particularly important in vertical heterostructures of 2D materials and enables a non-invasive way of designing nanoscale functionality, such as lateral heterojunctions, through the spatial control of substrate dielectrics [8,10,11].To exploit the full potential of tailoring Coulomb interactions through control of the dielectric environment, it is critical to understand its impact not only on the band gap but also on the valence and conduction band dispersions. The dispersion determines such basic properties as the effective masses of the carriers and the energy differences between different valleys within the Brillouin zone, and also affects the relative alignment between the valence and conduction bands of a homogeneous monolayer with spatially varying external dielectric screening. To date, experimental studies of dielectric engineering have mainly focused on optical spectroscopy or electronic transport measurements of TMDC monolay-ers, which only probe a small fraction of the full Brillouin zone. In general, however, perturbations to a material do not have the same effect on electronic states of different orbital character and can be expected to modify the band structure in different parts of the Brillouin zone differently.Here, through a combination of experiment and theory, we provide a generalized picture of the consequences of dielectric scree...

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The manipulation of two-dimensional materials via their dielectric environment offers novel opportunities to control electronic as well as optical properties and allows one to imprint nanostructures in a noninvasive way. Here we asses the potential of monolayer semiconducting transition-metal dichalcogenides (TMDCs) for Coulomb engineering in a material realistic and quantitative manner. We compare the response of different TMDC materials to modifications of their dielectric surrounding, analyze effects of dynamic substrate screening, i.e., frequency dependencies in the dielectric functions, and discuss inherent length scales of Coulombengineered heterojunctions. We find symmetric and rigid-shift-like quasiparticle band-gap modulations for both instantaneous and dynamic substrate screening. From this, we derive short-ranged self-energies for an effective multiscale modeling of Coulomb-engineered heterojunctions composed of a homogeneous monolayer placed on a spatially structured substrate. For these heterojunctions, we show that band-gap modulations on the length scale of a few lattice constants are possible, rendering external limitations of the substrate structuring more important than internal effects. We find that all semiconducting TMDCs are similarly well suited for these external and noninvasive modifications.

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