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 renormalization 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 geometries, the induced conduction-band potential and band-gap renormalization are given, demonstrating a curvature of the potential that is independent of the height of the deforming nanopillar. Additionally, with a semiclassical WKB approximation, the expected escape rate of electrons in the strain potential may be calculated as a function of the height of the deforming nanopillar. This approach is in accordance with experiment, supporting recent findings suggesting that increasing nanopillar height decreases the linewidth of the single-photon emitters observed at the tip of the pillar and predicting the shift in photon energy with nanopillar height for systems with consistent topography.