Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states

Typically, edge states in graphene are known to exist solely along zigzag edges. However, in this paper, we present a theoretical discovery of edge states along armchair edges in graphene under shear strain. This phenomenon arises from shear strain causing a separation between two inequivalent Dirac cones in the Brillouin zone (BZ) along the zigzag direction. Consequently, these armchair edge states appear as flat bands, connecting the two Dirac points at the two edges of armchair graphene nanoribbons (AGNRs). The length of these flat bands in the BZ and the penetration depth of the edge states are directly and inversely proportional to the strain, respectively. In monolayer AGNRs, possible magnetic configurations of flat bands resulting from electron-electron interactions are investigated. The edge-to-edge antiferromagnet (AFM) ground state is found in neutral AGNRs, while the AFM to ferromagnet (FM) transition can occur and be controlled by the strain in low-doped AGNRs. In gapped bilayer AGNRs, the armchair edge states evolve into quantum valley Hall edge states (QVHESs), which significantly improves the conductivity of QVHESs at realistic imperfect sample edges. These armchair edge states present a promising and tunable platform for exploring topological edge states in graphene.