Origin of the $\pi$-band replicas in the electronic structure of graphene grown on $4H$-SiC(0001)

The calculated electronic band structure of graphene is relatively simple, with a Fermi surface consisting only of six Dirac cones in the first Brillouin zone—one at each $\overline{K}$. In contrast, angle-resolved photoemission measurements of graphene grown on SiC(0001) often show six satellite Dirac cones surrounding each primary Dirac cone. Recent studies have reported two further Dirac cones along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ line, and argue that these are not photoelectron diffraction artifacts but real bands deriving from a modulation of the ionic potential in the graphene layer. Here we present measurements using linearly polarized synchrotron light which show all of these replicas as well as several additional ones. Using information obtained from dark corridor orientations and angular warping, we demonstrate that all but one of these additional features—including those previously assigned as real initial-state bands—are possible to explain by simple final-state photoelectron diffraction.

Figure 1

(a) The Fermi surface of a 1-ML graphene sample grown on a $4H$-SiC(0001) substrate using $p$-polarized 40-eV photons. (b) The same measurement presented with two different color scales in order to visualize all features. The positions of eight different Fermi pockets are highlighted within the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}\text{−}\overline{M}$ wedge. (c) $\left(E,k_Y\right)$ cuts through four of the features, each showing identical Dirac-like dispersions.

Figure 2

(a) The measurement data from Fig. 1, here visualized as an $E_B=1.3$ eV constant energy surface to emphasize the trigonal warping of the Dirac cones. (b) An $\left(E,k_X\right)$ cut through $k_Y=0$, from which the reversal of the dark corridor orientations is clear for the Dirac cones A and B compared to C and D.

Figure 3

(a),(b) Schematic depiction of the characteristic LEED pattern from sublimation grown graphene on $4H$-SiC(0001). Scattering vectors are shown corresponding to the graphene layer $\left(\overrightarrow{G}\right)$ and the SiC layer $\left(\overrightarrow{S}\right)$, as well as selected vectors from the $6\sqrt{3}$ and $6\times 6$ superlattices. (c) A $\mu$-LEED pattern $(E=45$ eV, 5-$\mu \mathrm{m}$ probing area) collected from a SiC(0001) sample prepared to have “zero monolayer” graphene coverage. The image was collected as part of an earlier study [15].

Figure 4

Examples of scattering processes which can scatter photoelectrons from one of the primary Dirac cones at $\overline{K}$ to the locations of replica features B–H. While scattering processes are shown as vector sums, the buffer layer reconstruction makes all of these possible as one-step scattering events.

Figure 5

(a) The Fermi surface recorded from a multilayer graphene sample grown on a $4H$-SiC(0001) substrate using $p$-polarized 40-eV photons. The locations of the eight features in the 1-ML sample are highlighted. (b) $\left(E,k_Y\right)$ cuts through features A–D. While the number and dispersion of the bands are the same for each feature, the relative intensities of the inner and outer bands vary strongly.

Figure 6

(a) Schematic of the polarization geometry. As the sample is rotated during the course of an ARPES measurement, the electric-field vector of $p$-polarized light evolves from being in the sample plane at normal incidence, to being out of plane at grazing incidence. (b) $\left(E,k_Y\right)$ cuts of the primary Dirac cone at $\overline{K_4}$ and the $\overrightarrow{6\times 6}$ satellites around it. While all six satellites should have identical intensity patterns, here it is clear that the relative intensity of the inner and outer bands depends on the $k_X$ location of the feature, i.e., the polar rotation of the sample.