Analytical results for the wrinkling of graphene on nanoparticles

A continuum elastic model, describing the wrinkling instability of graphene on substrate-supported silica nanoparticles [M. Yamamoto et al., Phys. Rev. X 2, 041018 (2012)2160-330810.1103/PhysRevX.2.041018], is analytically studied, and an exact analytical expression of the critical nanoparticle separation or the maximum wrinkle length is derived. Our findings agree with the scaling property of Yamamoto et al. but improve their results. Moreover, from the elastic model we find a pseudomagnetic field as a function of the wrinkling deflection, leading to the conclusion that the middle of the wrinkled graphene may have a zero pseudomagnetic field, in marked contrast with previous results.