Theory of Carbon Nanocones: Mechanical Chiral Inversion of a Micron-Scale Three-Dimensional Object

Abstract

Graphene cones have two degenerate configurations: their original shape and its inverse. When the apex is depressed by an external probe, the simulated mechanical response is highly nonlinear, with a broad constant-force mode appearing after a short initial Hooke's law regime. For chiral cones, the final state is an atomically exact chiral invert of the original system. If the local reflection symmetry of the graphene sheet is broken by the chemisorption of just five hydrogen atoms to the apex, then the maximal yield strength of the cone increases by $\sim 40\%$. The high symmetry of the conical geometry can concentrate micron-scale mechanical work with atomic precision, providing a way to activate specific chemical bonds.