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

Rode, J. C., D. Zhai, C. Belke, S. J. Hong, H. Schmidt, N. Sandler, and R. J. Haug. 2018. “Linking Interlayer Twist Angle to Geometrical Parameters of Self-Assembled Folded Graphene Structures”. 2D Materials.

Abstract

Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge—parameterized by a radius R—, and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. 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 analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.

Last updated on 09/17/2024