  We investigate how external screening shapes excitons in two-dimensional (2d)
semiconductors embedded in laterally structured dielectric environments. An
atomic scale view of these elementary excitations is developed using models
which apply to a variety of materials including transition metal
dichalcogenides (TMDCs). We find that structured dielectrics imprint a peculiar
potential energy landscape on excitons in these systems: While the ground-state
exciton is least influenced, higher excitations are attracted towards regions
with high dielectric constant of the environment. This landscape is "inverted"
in the sense that low energy excitons are less strongly affected than their
higher energy counterparts. Corresponding energy variations emerge on length
scales of the order of a few unit cells. This opens the prospect of trapping
and guiding of higher excitons by means of tailor-made dielectric substrates on
ultimately small spatial scales.
