Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

Owing to their atomic thickness and low bending rigidity, suspended two-dimensional (2D) materials are prone to wrinkle formation. Here, we use molecular dynamics (MD) simulations to probe the effect of these wrinkles on the nonlinear elasticity of atomically thin graphene membranes. We observe a stress-strain response that consists of two linear regions that are separated by a transition. It is found that this transition is sharp in membranes where wrinkles are formed by uneven stresses at the boundaries. However, when wrinkles are formed by crystal defects, this nonlinear transition is seen to be more gradual. To capture these effects, we use a phenomenological model based on experimentally measurable quantities. We demonstrate the model's fidelity by fitting it to the MD simulated nonlinear response of many graphene membranes providing evidence that the sharpness of the transition between the linear regions in the stress-strain response is a measure of the type of wrinkles and can be quantified by our model.

Transferring graphene flakes onto hexagonal boron nitride (h-BN) has become a common approach for fabricating graphene/h-BN heterostructures. Controlling the alignment between graphene and h-BN lattices is difficult to achieve and the h-BN/graphene interface is prone to contamination in this complicated process. Direct synthesis of graphene on h-BN is a rapidly growing alternative. In situ grown graphene is individually tailored to conform to the specific h-BN flake, hence the limitations of the conventional transfer-based fabrication approach are overcome. Developed processes promise improved scalablity of the device fabrication, eventually suitable for industrial applications. The developments in the field, from inception to current status is the focus of this review. How the field is progressing to overcome existing challenges is discussed together with its future prospects.