Phonon bandgap engineering of strained monolayer MoS₂.

The phonon band structure of monolayer MoS₂ is characteristic of a large energy gap between acoustic and optical branches, which protects the vibration of acoustic modes from being scattered by optical phonon modes. Therefore, the phonon bandgap engineering is of practical significance for the manipulation of phonon-related mechanical or thermal properties in monolayer MoS₂. We perform both phonon analysis and molecular dynamics simulations to investigate the tension effect on the phonon bandgap and the compression induced instability of the monolayer MoS₂. Our key finding is that the phonon bandgap can be narrowed by the uniaxial tension, and is completely closed at ε = 0.145; while the biaxial tension only has a limited effect on the phonon bandgap. We also demonstrate the compression induced buckling for the monolayer MoS₂. The critical strain for buckling is extracted from the band structure analysis of the flexure mode in the monolayer MoS₂ and is further verified by molecular dynamics simulations and the Euler buckling theory. Our study illustrates the uniaxial tension as an efficient method for manipulating the phonon bandgap of the monolayer MoS₂, while the biaxial compression as a powerful tool to intrigue buckling in the monolayer MoS₂.