Strain-induced band-gap engineering of graphene monoxide and its effect on graphene

Using first-principles calculations we demonstrate the feasibility of band-gap engineering in two-dimensional crystalline graphene monoxide (GMO), a recently reported graphene-based material with a 1:1 carbon/oxygen ratio. The band gap of GMO, which can be switched between direct and indirect, is tunable over a large range (0–1.35 eV) for accessible strains. Electron and hole transport occurs predominantly along the zigzag and armchair directions (armchair for both) when GMO is a direct- (indirect-) gap semiconductor. A band gap of ∼0.5 eV is also induced in graphene at the $K$′ points for GMO/graphene hybrid systems.

Figure 1

Structure and difference charge density of GMO. (a) Perspective and top views of GMO in a 3 × 3 cell with lattice parameters labeled. C (O) atoms are represented by yellow (red) balls; all C atoms are in the same plane. (b) Side views of the difference between the self-consistent and overlapping atomic electron densities (△$n$ $=$ $n_{\mathrm{CO}}$ − $n_{\mathrm{C}}$ − $n_{\mathrm{O}}$) of GMO. Light blue and green isosurfaces (±0.05 $e$/$a_{\mathrm{B}}$${}^3$) indicate accumulation and depletion of electrons, respectively.

Figure 2

(a) Distortion energies relative to the fully relaxed GMO structure per CO formula unit as functions of the structural parameters α and $d_{\mathrm{O}-O}$ given in Fig. 1a. The black star represents the lattice parameters of the fully relaxed structure; the blue line indicates a constant $a_0$ $=$ 3.10 Å. (b) Calculated band gap of GMO as a function of α and $d_{\mathrm{O}-O}$. The calculated crossover between direct and indirect gap is indicated by the dashed line. Calculated bands for $a_0$ $=$ 3.10 Å in (c) α $=$ 130° and (d) α $=$ 125°. The inset in (c) shows the symmetry lines and points in the Brillouin zone for GMO. Since the point group symmetry of GMO is $D_{2h}$, compared with the $D_{6h}$ symmetry of graphene, the $K$′ point in GMO has no additional symmetry compared to other points along Δ′. The effective mass labels indicate light and. heavy electrons ($m^{*}$${}_{Le}$, $m^{*}$${}_{He}$) and holes ($m^{*}$${}_{Lh}$, $m^{*}$${}_{Hh}$).

Figure 3

Charge density isosurfaces (0.05 $e$/$a_{\mathrm{B}}$${}^3$) of states at the top of the valence band (light green) and at the bottom of the conduction band (blue) in top and side views. (a) and (c) IGMO: ${\Gamma }_{\mathrm{C}1}$ and $X_{\mathrm{V}1}$ [cf. Fig. 3a]; (b) and (d) DGMO: $X_{\mathrm{C}1}$ and $X_{\mathrm{V}1}$ [cf. Fig. 3b].

Figure 4

Electron (black squares) and hole (red circles) effective masses are shown for anisotropic GMO. The effective masses of carriers with respect to lattice angles are evaluated from quadratic fits to the band dispersion. The transition from IGMO to DGMO is ∼126°.

Figure 5

(a) Interface model of graphene and GMO with $d_{\mathrm{O}-O}$ [cf. Fig. 1a] fixed to the lattice constant of graphene (2.46 Å). The 1 × 1 Brillouin zones with labels for the graphene and GMO regions are indicated. (b) and (c) $k$-projected band structures for graphene and GMO, respectively, in the middle of each region. The inset in (b) is a magnified view of the bands around $K$′ enclosed in the yellow rectangle. (The $k$ projection decomposes the supercell wave functions into momentum components of the 1 × 1 cells, thus “unfolding” the bands; the resulting states are then spatially integrated to give the relative intensities—varying from blue to red—shown.)