GRAPHENE Across the border

The topological nature of a certain type of grain boundary in polycrystalline graphene may be used to customize the electrical transport properties. The zone folding method involves folding the 2D band structure along the 1D band that follows the grain boundary. The folded 2D graphene band is then projected on the 1D mini-band, reflecting the periodic structure imposed by the periodicity of the grain boundary. A similar zone-folding approach is applied to nanotubes to understand the chirality dependence of metallic and semi-conducting nanotubes. The zone-folding approach in graphene result in two types of folded 1D band structure, depending on the chiral nature of the vector d, which is determined by the atomic lattice vectors in each domain. Matching the relative chiral nature of each graphene domain across the boundary leads to two different categories of the grain boundary that includes type I, where both sides of the grain boundary has similar chirality, and type II, where the relative chirality is different.