  The observation of quantum light emission from atomically thin transition
metal dichalcogenides has opened a new field of applications for these material
systems. The corresponding excited charge-carrier localization has been linked
to defects and strain, while open questions remain regarding the microscopic
origin. We demonstrate that the bending rigidity of these materials leads to
wrinkling of the two-dimensional layer. The resulting strain field facilitates
strong carrier localization due to its pronounced influence on the band gap.
Additionally, we consider charge carrier confinement due to local changes of
the dielectric environment and show that both effects contribute to modified
electronic states and optical properties. The interplay of surface wrinkling,
strain-induced confinement, and local changes of the dielectric environment is
demonstrated for the example of nanobubbles that form when monolayers are
deposited on substrates or other two-dimensional materials.
