Theory of strain-induced confinement in transition metal dichalcogenide monolayers

Recent experimental studies of out-of-plane straining geometries of\ntransition metal dichalchogenide (TMD) monolayers have demonstrated sufficient\nband gap renormalisation for device application such as single photon emitters.\nHere, a simple continuum-mechanical plate-theory approach is used to estimate\nthe topography of TMD monolayers layered atop nanopillar arrays. From such\ngeometries, the induced conduction band potential and band gap renormalisation\nis given, demonstrating a curvature of the potential that is independent of the\nheight of the deforming nanopillar. Additionally, with a semi-classical WKB\napproximation, the expected escape rate of electrons in the strain potential\nmay be calculated as a function of the height of the deforming nanopillar. This\napproach is in accordance with experiment, supporting recent findings\nsuggesting that increasing nanopillar height decreases the linewidth of the\nsingle photon emitters observed at the tip of the pillar, and predicting the\nshift in photon energy with nanopillar height for systems with consistent\ntopography.\n