Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures

Previous studies have shown the possibility of obtaining folded bilayer graphene ribbons through spontaneous self-tearing and peeling from a substrate [1]. However, the effect of interlayer twist angle has been neglected. Here we investigate the morphology of spontaneously self-grown nanoribbon structures using AFM. Data reveal similar twist angle dependence of the width and interlayer separation, as well as a width-dependent fold radius. As the self-growth involves bilayer formation, bending, tearing and substrate peeling processes, these observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an explicit expression for the radius-width dependence that predicts a renormalized bending rigidity and stand in good agreement with experimental observations. The newly found relations between these geometrical parameters suggest a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.

[1] J. Annett and G. Cross, Nature 535, 271 (2016).