Theory of Strain-Induced Confinement in Transition Metal Dichalcogenide Monolayers*

Recent experimental studies of out-of-plane straining geometries of transition metal dichalchogenide (TMD) monolayers have demonstrated sufficient band gap renormalisation for device application such as single photon emitters. Here, a simple continuum-mechanical plate-theory approach is used to estimate the topography of TMD monolayers layered atop nanopillar arrays. From such topologies, the induced conduction band potential and band gap renormalisation is given, demonstrating a potential shape that is independent of the height of deforming nanopillar. Additional, with a semi-classical WKB approximation, the expected leakage of the strain potential may be estimated as a function of the height of the deforming nanopillar. This straight forward approach is in accordance with experiment, supporting recent findings suggesting that nanopillar height improves linewidth of the single photon emitters observed at the tip of the pillar, yet has no discernible influence over the wavelengths of the emitted photons.