\textit{Giant blue shifted photoluminescence peak from the edges of CVD grown monolayer MoS}$_{2}$

To probe the electronic and optical properties of direct band-gap monolayer transition metal dichalcogenides, such as band structure and excitons, micro-photoluminescence spectroscopy has become an attractive and standard tool. Here, we present our experimental work on spatial scanning of photoluminescence of monolayer MoS$_{\mathrm{2}}$ grown by chemical vapor deposition (CVD) using an ultrasmall blue laser (wavelength 405 nm) beam spot with beam diameter as small as $\sim 200$ nm. We have observed a giant blue shift, as large as $\sim 40$ nm or $\sim 100$ meV, of the $A$-excitonic peak in the photoluminescence spectra from the edges when compared to luminescence from the inside. This giant blue shift may result from the following: (i) compressive strain at the edges; (ii) the enhanced dielectric screening caused by the increased electron density at the metallic Mo-edges; and (iii) chemical impurities.