We perform both molecular dynamics simulations and theoretical analysis to study the sensitivity of the graphene nanomechanical resonator based mass sensors, which are actuated following the global extended mode or the localized edge mode. We find that the mass detection sensitivity corresponding to the edge mode is about three times higher than that corresponding to the extended mode. Our analytic derivations reveal that the enhancement of the sensitivity originates in the reduction of the effective mass for the edge mode due to its localizing feature.

We derive analytical expressions for the Young's modulus and the Poisson's ratio of the graphene nanoribbon, in which free edges are warped by the compressive edge stress. Our analytical formulas explicitly illustrate the reduction of the Young's modulus by the warped free edges, leading to the obvious width dependence for the Young's modulus of the graphene nanoribbon. The Poisson's ratio is also reduced by the warped free edges, and negative Poisson's ratio can be achieved in the graphene nanoribbon with an ultra-narrow width. These results are comparable with previous theoretical works.

Directional motion is one of the most fundamental motions in the nature, which is driven by specific types of gradients. The transition metal dichalcogenides graded lateral heterostructure is a valuable semiconductor playing crucial roles in electronic and optoelectronic devices. This lateral heterostructure has a graded composition and is thus a promising candidate to drive possible directional motions. Here, we perform molecular dynamics simulations to demonstrate the directional motion of a graphene sheet on top of the MoS2–WSe2 graded lateral heterostructure. It is quite interesting that the direction for the diffusion is sensitive to the graphene sheet’s initial location, which is in two different regions. The graphene sheet diffuses in opposite directions for the initial location that falls in different regions. We derive an analytic formula for the interlayer coupling potential, which discloses the underlying mechanism for the dependence of the directional motion on the initial location of the graphene sheet. These results shall be varifiable by present experimental set ups and may be valuable for the application of the transition metal dichalcogenides graded lateral heterostructure in practical electronic devices.

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