3D Strain in 2D Materials: To What Extent is Monolayer Graphene Graphite?

This work addresses a fundamental question: To what extent is graphene graphite? In particular does 2D graphene have many of the same 3D mechanical properties as graphite, such as the bulk modulus and elastic constant c_{33}? We have obtained, for the first time, unambiguous Raman spectra from unsupported monolayer graphene under pressure. We have used these data to quantify the out-of-plane stiffness of monolayer graphene, which is hard to define due to its 2D nature. Our data indicate a first physically meaningful out-of-plane stiffness of monolayer graphene, and find it to be consistent with that of graphite. We also report a shift rate of the in-plane phonon frequency of unsupported monolayer graphene to be 5.4  cm^{-1} GPa^{-1}, very close to that of graphite (4.7  cm^{-1} GPa^{-1}), contrary to the previous value for supported graphene. Our results imply that monolayer graphene has similar in-plane and out-of-plane stiffnesses, and anharmonicities to graphite.