Under pressure: Control of strain, phonons and bandgap opening in rippled graphene

Two-dimensional (2D) layers like graphene are subject to long-wavelength fluctuations that manifest themselves as strong height fluctuations (ripples). In order to control the ripples, their relationship with external strain needs to be established. We therefore perform molecular dynamics (MD) of suspended graphene, by the use of a newly developed force field model (MMP) that we prove to be extremely accurate for both C Diamond and Graphene. The MMP potential successfully reproduces the energy of the σ-bonds in both sp³ and sp² configuration. Our MD simulations and experimental electron microscopy analysis reveal that ordered and static ripples form spontaneously as a direct response to external pressure. Furthermore the morphology of graphene and strain response of the crystal bonds differ depending on the particular directions where external pressure is present. Different regions of the strained graphene sheet are then investigated by tight-binding. Localised bandgap opening is reported for specific strain combinations, which also results in particular signatures in the phonon spectrum. Such controllable morphological changes can therefore provide a means to practically control and tune the electronic and transport properties of graphene for applications as optoelectronic and nanoelectromechanical devices.