Theoretical Studies of Local Strain-Induced Heterogeneity in Electronic and Phononic Properties of WSe2 Nanostructures

Since the electronic and optical properties of two-dimensional (2D) transition-metal dichalcogenides (TMDs) are highly susceptible to mechanical deformations, it is very important to understand how the geometries, band structures, and excitonic dynamics are influenced under different strain conditions in TMDs, especially for nanowrinkles and nanobubbles with complex inhomogeneities in real space. Here, we proposed a general model to explore the influence of local strains on both the electronic and phononic band structures for various nanostructures. We demonstrate that the electronic bandgaps in nanotubes and nanowrinkles can be accurately predicted from the monolayer results by considering both the effects of tensile strain and curvature-induced flexoelectricity. The frequency shifts of intrinsic vibrational modes can be adopted as the indicator of local strains, while the newly emerged radial-breathing-like mode, originated from the out-of-plane acoustic phonons in a monolayer, is quite sensitive to the magnitude of curvature. This model is further generalized to the nanobubble structure, exhibiting smaller electronic bandgaps and lower vibrational frequencies in general, except for the radial-breathing-like mode, which shows the largest vibrational frequency at the center, consistent with the spatial distributions of local strains and curvatures in the nanobubble. Our findings establish a framework for predicting strain-induced spectral changes in complex nanostructures, guiding the design of strain-engineered optoelectronic devices based on 2D materials.