Band Gap of Strained Graphene Nanoribbons

The band structures of strained graphene nanoribbons (GNRs) are examined by a tight binding Hamiltonian that is directly related to the type and strength of strains. Compared to the two-dimensional graphene whose band gap remains close to zero even if a large strain is applied, the band gap of graphene nanoribbon (GNR) is sensitive to both uniaxial and shears strains. The effect of strain on the electronic structure of a GNR strongly depends on its edge shape and structural indices. For an armchair GNR, uniaxial weak strain changes the band gap in a linear fashion, and for a large strain, it results in periodic oscillation of the band gap. On the other hand, shear strain always tend to reduce the band gap. For a zigzag GNR, the effect of strain is to change the spin polarization at the edges of GNR, thereby modulate the band gap. A simple analytical model is proposed to interpret the band gap responds to strain in armchair GNR, which agrees with the numerical results.