Thermal control of graphene morphology: a signature of its intrinsic surface tension

The surface tension $\sigma$ of free-standing graphene is studied by path-integral simulations as a function of the temperature and the in-plane stress. Even if the applied stress vanishes, the membrane displays a finite surface tension $\sigma$ due to the coupling between the bending oscillations and the real area of the membrane. Zero-point effects for $\sigma$ are significant below 100 K. Thermal cooling drives the membrane from a planar to a wrinkled morphology. Upon heating the change is reversible and shows hysteresis, in agreement to recent experiments performed on supported graphene.