Topological Regard to Graphene: Elucidating the Morphology-Strain Correlation

Graphene, dubbed as a two-dimensional material represents the topological concept of "surface" embedded in a three-dimensional space. This regard enables to employ existing theories/tools in topology to understand different properties/observations in graphene. Under the light of the long-established "Gauss's Theorema Egregium" we study wrinkled graphene, observing a peculiar correlation between morphology and strain distribution. Compressing graphene on water serves as an effectual platform to realize wrinkles; we explain the evolution of the wrinkles and the global distribution of the strain field while progressing the compression. The introduced platform in this paper offers an efficient approach to precisely control the generation and evolution of the wrinkles, transforming into a naturally occurring 3D landscape as a result of graphene buckling.