Impact of local stacking on the graphene-impurity interaction: Theory and experiments

We investigate the graphene-impurity interaction problem by combining experimental—scanning tunneling microscopy (STM) and spectroscopy (STS)—and theoretical—Anderson impurity model and density functional theory (DFT) calculations—techniques. We use graphene on the SiC$\left(000\overline{1}\right){(2\times 2)}_C$ reconstruction as a model system. The SiC substrate reconstruction is based on silicon adatoms. Graphene mainly interacts with the dangling bonds of these adatoms which act as impurities. Graphene grown on SiC$\left(000\overline{1}\right){(2\times 2)}_C$ shows domains with various orientations relative to the substrate so that very different local graphene/Si adatom stacking configurations can be probed on a given grain. The position and width of the adatom (impurity) state can be analyzed by STM/STS and related to its local environment owing to the high-bias electronic transparency of graphene. The experimental results are compared to Anderson's model predictions and complemented by DFT calculations for some specific local environments. We conclude that the adatom resonance shows a smaller width and a larger shift toward the Dirac point for an adatom at the center of a graphene hexagon than for an adatom just on top of a C graphene atom.

Figure 1

(a) Schematic representation of the SiC$\left(000\overline{1}\right){(2\times 2)}_C$ surface reconstruction. The unit cell (dashed diamond cell) contains one Si adatom with an empty DB (dashed line) and one C restatom with a filled DB (dotted line). (b) Schematic side view of the system $G/2\times 2$ with the $p_z$ graphene orbitals and the empty (filled) DB on the reconstruction adatom (restatom). (c) Schematic top view of the graphene/adatom stacking in case of a rotation angle $\alpha =16{}^{\circ }$. The common pseudocell (black solid line) contains various stacking configurations.

Figure 2

(a),(b) $3\times 3$ nm${}^2$ Dual-bias STM images of a $G/2\times 2$ island. At high bias, images show the substrate reconstruction states (solid line unit cell). Panel (a) [(b)] exhibits the filled (empty) states associated to the restatom (adatom). (c),(d) $6\times 6$ nm${}^2$ dual-bias STM images of the same $G/2\times 2$ island as in (a) and (b). Panel (c) exhibits the adatom empty states while (d) exhibits the graphene overlayer LDOS near $E_F$. A moiré pattern (solid line cell) is visible on both images (periodicity $P=3.0\pm 0.3$ nm, measured stacking angle $\alpha =16\pm 1^{\circ }$).

Figure 3

Tunneling bias dependance of the moiré pattern (pseudocell in solid line) contrast, $7\times 7$ nm${}^2$ constant current mode images. (a) STM image at the reference tunneling bias $V_S=+1.5$ V, (b)–(e) and (g) being extracted from dual-bias images in order to check the structure positions. (b) Low-bias image showing the unperturbed (corner of the moiré pseudocell) and perturbed (within the moiré pseudocell) graphene zones. (c)–(e) Evolution of the moiré contrast with $V_S$ on adatom empty states. Panel (d) shows an asymmetry contrast between the top and bottom halves of the moiré pseudocell. (f) Schematic representation of the graphene/reconstruction stacking deduced from (a), (b), and (g). Honeycomb contrast on (b) corresponds to hollow graphene/adatom and top graphene/restatom stacking. Perturbed graphene regions correspond to top graphene/adatom stacking with top (hollow) graphene/restatom stacking in the top (bottom) half of the moiré pseudocell. (g) Moiré contrast on restatom states (filled states).

Figure 4

CITS data on the same island as in Fig. 3. (a) $7\times 7$ nm${}^2$ constant current image at the CITS stabilization parameters (moiré pseudocell in black). (b) Conductance image revealing the moiré pattern. (c) $I\left(V\right)$ curves spatially averaged over $2.5$ nm${}^2$ (20 spectra), on the three different graphene/reconstruction stacking regions [see crosses in (a) and (b): graphene/adatom: hollow (red) graphene/adatom top and graphene/restatom hollow (blue) graphene/restatom top (black)]. (d) Corresponding conductance curves. Each curve shows a peaked structure ascribed to the adatom level, at $V_S=+1.35$ V (red), $V_S=+1.52$ V (blue), and $V_S=+1.61$ V (black).

Figure 5

The graphene/adatom interaction in the framework of the Anderson model. (a) The top (left) and hollow (right) configurations. (b) Interacting level energy in both hollow (${\tilde{\omega }}_{AA}^H$) and top (${\tilde{\omega }}_{AA}^T$) configurations and their relative shift ${\tilde{\omega }}_{AA}^H-{\tilde{\omega }}_{AA}^T$, for ${\omega }_{AA}=1$ eV and $V=1$ eV as a function of $\alpha$. (c) Real part of the adatom self-energy in the top ($T_{\alpha }$) and hollow ($H_{\alpha }$) configurations for various $\alpha ⩾0.5$ (and $\alpha =0$ in the top configuration) and $V=1$ eV. The gray straight lines represent $\omega -{\omega }_{AA}$ for ${\omega }_{AA}=1$, $1.6$, and 2 eV. (d) Imaginary part of the adatom self-energy in the top ($T_{\alpha }$) and hollow ($H_{\alpha }$) configurations for various $\alpha ⩾0.5$ (and $\alpha =0$ in the top configuration) and $V=1$ eV. Insert: $\text{Im}\left[{\Sigma }^T\left(\omega \right)\right]/\text{Im}\left[{\Sigma }^H\left(\omega \right)\right]$ for various $\alpha ⩾0.5$ (with the same color code as for $\text{Im}\left[\Sigma \right]$). (e) Normalized DOS associated to the adatom in both top and hollow configurations with ${\omega }_{AA}=1.6$ eV, $V=1$ eV, and $\alpha =0.8$. Inset: Residual DOS at low energy.

Figure 6

Ab initio electronic structure calculations of graphene on SiC$\left(000\overline{1}\right)(2\times 2)$. (a),(b) Top view of the two considered supercells, displaying top (A4), slightly shifted top (A1-3), bridge (B1-3), and hollow (B4) graphene/adatom stacking configurations. Only the last SiC bilayer, the adatoms and the graphene layer are represented. (c),(d) Respective band-structure calculations in the energy range spanning the adatom low-dispersive bands. (e) Calculated LDOS for the A3-4 and B3-4 adatoms. (f),(g) Maps of ${\left|\Psi \right|}^2$ integrated over the energy range $[+0.5$ eV$,+1.0$ eV$]$ taken just above the graphene atoms, for the configurations given in (a) and (b). Contrast is reversed with respect to Figs. 2d and 3b: higher density is darker. The adatom positions are indicated by dashed circles.