Electronic structure of graphene on single-crystal copper substrates

The electronic structure of graphene on Cu(111) and Cu(100) single crystals is investigated using low-energy electron microscopy, low-energy electron diffraction, and angle-resolved photoemission spectroscopy. On both substrates the graphene is rotationally disordered and interactions between the graphene and substrate lead to a shift in the Dirac crossing of $\sim$$-$0.3 eV and the opening of a $\sim$250 meV gap. Exposure of the samples to air resulted in intercalation of oxygen under the graphene on Cu(100), which formed a ($\sqrt{2}\times 2\sqrt{2}$)R45${}^{\mathrm{o}}$ superstructure. The effect of this intercalation on the graphene $\pi$ bands is to increase the offset of the Dirac crossing ($\sim$$-$0.6 eV) and enlarge the gap ($\sim$350 meV). No such effect is observed for the graphene on the Cu(111) sample, with the surface state at $\Gamma$ not showing the gap associated with a surface superstructure. The graphene film is found to protect the surface state from air exposure, with no change in the effective mass observed, as for one monolayer of Ag on Cu(111).

Figure 1

Experimental fermi surface and $\pi$ band structure obtained from graphene on $(6\sqrt{3}\times 6\sqrt{3})$R30${}^{\circ }$ C-SiC (a i, ii, and iii) for comparison to a semiempirical model (b i, ii, and iii). The model employs a first nearest-neighbor tight binding model for the bare (unbroadened) bands with the parameters (${\gamma }_0=-3.24$ eV, $s_0=0.0425$ eV, and ${\epsilon }_{2p}=-0.47$ eV) determined from a fit to the experimental data. Broadening is performed using the self-energy, obtained by a fit to the experimental data in the $\Gamma$-K direction, and experimental broadening of 25 meV and 0.01 Å${}^{-1}$. The simulation and experiment agree qualitatively.

Figure 2

LEEM/LEED characterization of a nearly complete single-layer graphene film on Cu(111). (a) LEEM image with a 20-$\mu$m field of view. Bright dots are nucleation sites and bright lines are boundaries between graphene islands. (b) LEED from a 20-$\mu$m-diameter area of (a). First-order diffraction spot of Cu marked by red arrow and portion of graphene arc marked by blue arrow.

Figure 3

LEEM/LEED characterization of single-layer graphene film on Cu(100). (a) LEEM image with a 20-$\mu$m field of view. Dark lines are boundaries between graphene islands. (b) LEED from 20-$\mu$m-diameter area of as-grown graphene. One graphene arc marked by a blue arrow. (c) LEED from a 2-$\mu$m-diameter area of air-exposed sample. Diffraction spots of Cu, graphene, and intercalated O are denoted by red, blue, and green arrows, respectively.

Figure 4

Experimental Fermi surface (a) obtained from graphene on single-crystal Cu(111). Also presented is the experimental spectral function (b), semiemperical model spectral function (c), energy distribution curves (d), and momentum distribution curves (e) obtained along the white line in (a) (Cu Brillouin zone $\Gamma$-K direction). The graphene $\pi$ bands calculated from a first nearest-neighbor tight binding model (${\gamma }_0=-3.24$ eV, $s_0=0.0425$ eV, and ${\epsilon }_{2p}=-0.3$ eV) are overlayed as the large dashed blue lines. A parabolic fit to the Cu(111) surface states is also shown (small dashed yellow lines). All other unmarked bands are due to the bulk Cu. The graphene Fermi surface is observed as an uninterrupted ring due to rotationally disordered graphene domains. The preferential alignment (higher intensity) of the domains along the $\Gamma$-K direction is also observed in LEED.

Figure 5

Experimental Fermi surface (a) obtained from graphene on single-crystal Cu(100). Also presented is the experimental spectral function (b), semiemperical model spectral function (c), energy distribution curves (d), and momentum distribution curves (e) obtained along the white line in (a) (Cu Brillouin zone $\Gamma$-K direction). The graphene $\pi$ bands calculated from a first nearest-neighbor tight binding model (${\gamma }_0=-3.24$ eV, $s_0=0.0425$ eV, and ${\epsilon }_{2p}=-0.3$ eV) are overlayed as the dash-dot blue and dash-dot dot green lines, respectively. All other unmarked bands are due to the bulk Cu. The graphene Fermi surface is observed as an uninterupted ring due to rotationally disordered graphene domains.

Figure 6

The energy distribution curves (dashed red lines) obtained at the $K$ point from the semiempirical model for a range of simulated band gaps (solid blue lines) are presented for (a) Cu(111), together with a single-band model ${\mathrm{G}}_{111}$ whose gap $E_g$(${\mathrm{G}}_{111}$) is varied, and [(b) and (c)] for Cu(100), which is compared to a two-band model ${\mathrm{G}}_{100}^{\mathrm{A}}$, ${\mathrm{G}}_{100}^{\mathrm{B}}$. In (b), the gap $E_g$(${\mathrm{G}}_{100}^{\mathrm{B}}$) is varied for fixed $E_g$(${\mathrm{G}}_{100}^{\mathrm{A}}$$)=250$ meV, while in (c), the gap $E_g$(${\mathrm{G}}_{100}^{\mathrm{A}}$) is varied for fixed $E_g$(${\mathrm{G}}_{100}^{\mathrm{B}}$$)=350$ meV. In all panels, the light blue lines represent best-fit models to the data.

Figure 7

Detailed experimental band structure of the Cu(111) surface state. The dashed yellow line denotes the parabolic fit used to determine the values in Table .