Band structure engineering of graphene by strain: First-principles calculations

We have investigated the electronic structure of graphene under different planar strain distributions using the first-principles pseudopotential plane-wave method and the tight-binding approach. We found that graphene with a symmetrical strain distribution is always a zero band-gap semiconductor and its pseudogap decreases linearly with the strain strength in the elastic regime. However, asymmetrical strain distributions in graphene result in opening of band gaps at the Fermi level. For the graphene with a strain distribution parallel to C-C bonds, its band gap continuously increases to its maximum width of 0.486 eV as the strain increases up to 12.2%. For the graphene with a strain distribution perpendicular to C-C bonds, its band gap continuously increases only to its maximum width of 0.170 eV as the strain increases up to 7.3%. The anisotropic nature of graphene is also reflected by different Poisson ratios under large strains in different directions. We found that the Poisson ratio approaches to a constant of 0.1732 under small strains but decreases differently under large strains along different directions.

Figure 1

(Color online) (a) Graphene system with symmetrical strain distribution, (b) asymmetrical strain distribution perpendicular to C-C bonds, and (c) asymmetrical strain distribution parallel to C-C bonds. Corresponding primitive cells (in black), reciprocal lattices (in red dashed), Brillouin zones [in blue (grey)], and irreducible Brillouin zones [in yellow (light grey)] are illustrated below the deformed lattices. $\Gamma$, $K$, $M$, $R$, and $S$ are the high symmetrical points. $L_x$ and $L_y$ are the half diagonal lengths of the primitive cells.

Figure 2

(Color online) (a) The band structure, DOS, and ELF for symmetrical graphene systems with different values of lattice constant. (b) The pseudogap width (arrow) as a function of lattice constant.

Figure 3

(Color online) (a) The band structure, PDOS, and ELF for the graphene systems with asymmetrical strain distributions parallel to C-C bonds. (b) $L_x$ as a function of $L_y$. (c) The band-gap width as a function of $L_y$.

Figure 4

(Color online) Band structures of the asymmetrical graphene system with $L_y=0.2296\text{nm}$ calculated by the first-principles method (curves) and the tight-binding method (symbols).

Figure 5

(Color online) (a) The band structure, PDOS, and ELF for the graphene systems with asymmetrical strain distributions perpendicular to C-C bonds. (b) $L_y$ as a function of $L_x$. (c) The band-gap width as a function of $L_x$.

Figure 6

(Color online) Poisson ratios of graphene under strains parallel to or perpendicular to C-C bonds.