Hierarchy of graphene wrinkles induced by thermal strain engineering

Here, we study hierarchy of graphene wrinkles induced by thermal strain engineering and demonstrate that the wrinkling hierarchy can be accounted for by the wrinklon theory. We derive an equation λ = (ky)^0.5, explaining evolution of wrinkling wavelength λ with the distance to the edge y observed in our experiment by considering both bending energy and stretching energy of the graphene flakes. The prefactor k in the equation is determined to be about 55 nm. Our experimental result indicates that the classical membrane behavior of graphene persists down to about 100 nm of the wrinkling wavelength.