Mutual influence of uniaxial tensile strain and point defect pattern on electronic states in graphene

The study deals with electronic properties of uniaxially stressed mono- and multi-layer graphene sheets with various kinds of imperfection: point defects modelled as resonant (neutral) adsorbed atoms or molecules, vacancies, charged impurities, and local distortions. The presence of randomly distributed defects in a strained graphene counteract the band-gap opening and even can suppress the gap occurs when they are absent. However, impurity ordering contributes to the band gap appearance and thereby reopens the gap being suppressed by random dopants in graphene stretched along zigzag-edge direction. The band gap is found to be non-monotonic with strain in case of mutual action of defect ordering and zigzag deformation. Herewith, the minimal tensile strain required for the band-gap opening (approximate to 12.5%) is smaller than that for defect-free graphene (approximate to 23%), and band gap energy reaches the value predicted for maximal nondestructive strains in the pristine graphene. Effective manipulating the band gap in graphene requires balanced content of ordered dopants: their concentration should be sufficient for a significant sublattice asymmetry effect, but not so much that they may suppress the band gap or transform it into the quasi-(or pseudo-) gap.