Stable hydrogenated graphene edge types: Normal and reconstructed Klein edges

Abstract

Hydrogenated graphene edges are assumed to be either armchair, zigzag, or a combination of the two. We show that the zigzag is not the most stable fully hydrogenated edge structure along the $\ensuremath{\langle}2\overline{1}\overline{1}0\ensuremath{\rangle}$ direction. Instead hydrogenated Klein and reconstructed Klein based edges are found to be energetically more favorable, with stabilities approaching that of armchair edges. These new structures ``unify'' graphene edge topology, the most stable flat hydrogenated graphene edges always consisting of pairwise bonded C${}_{2}$H${}_{4}$ edge groups, irrespective of the edge orientation. When edge rippling is included, CH${}_{3}$ edge groups are most stable. These new fundamental hydrogen-terminated edges have important implications for graphene edge imaging and spectroscopy, as well as mechanisms for graphene growth, nanotube cutting, and nanoribbon formation and behavior.