Density-functional study of edge stress in graphene

The definition of edge stress is introduced in order to quantify the energy cost to deform a pre-existing edge in a two-dimensional crystal. Using density-functional ab initio calculations, edge stresses, as well as edge energies, are determined for the armchair and zigzag edges in graphene. It is found that both edges are under compression along the edge and the magnitude of compressive edge stress of armchair edge is larger than that of zigzag edge. In addition, hydrogen termination results in stress-free state for both edges. This excess edge quantity is expected to contribute to understanding various edge-related phenomena in graphene such as edge reconstructions and edge functionalizations.