Origin of Anomalous Electronic Structures of Epitaxial Graphene on Silicon Carbide

On the basis of first-principles calculations, we report that a novel interfacial atomic structure occurs between graphene and the surface of silicon carbide, destroying the Dirac point of graphene and opening a substantial energy gap there. In the calculated atomic structures, a quasiperiodic $6\times 6$ domain pattern emerges out of a larger commensurate $6\sqrt{3}\times 6\sqrt{3}R30°$ periodic interfacial reconstruction, resolving a long standing experimental controversy on the periodicity of the interfacial superstructures. Our theoretical energy spectrum shows a gap and midgap states at the Dirac point of graphene, which are in excellent agreement with the recently observed anomalous angle-resolved photoemission spectra. Beyond solving unexplained issues in epitaxial graphene, our atomistic study may provide a way to engineer the energy gaps of graphene on substrates.

Figure 1

(a) Side and (b) top views of the atomic structure of the buffer layer with the $6\sqrt{3}\times 6\sqrt{3}R30°$ periodicity. The $6\sqrt{3}\times 6\sqrt{3}R30°$ supercell is denoted with blue lines and the $1\times 1$ surface unit cell of $4H\mathrm{\text{−}}\mathrm{SiC}(0001)$ with red. The carbon atoms in the buffer layer are denoted with black spheres and the silicon and the carbon atoms in the $4H\mathrm{\text{−}}\mathrm{SiC}$ with orange and green spheres, respectively. (c) Bonding characteristics of carbon atoms in the buffer layer. Carbon atoms with (without) $\sigma$-bonding to surface silicon atoms are represented with gray (black) dots. The $\pi$-bonds, represented by black lines, form a superhexagonal pattern. Four times the $6\sqrt{3}\times 6\sqrt{3}R30°$ periodicity is drawn in order to display the superhexagons clearly. The blue arrows are the unit vectors of the $6\sqrt{3}\times 6\sqrt{3}R30°$ supercell.

Figure 2

(a) Simulated spectrum for ARPES of the buffer layer on top of $4H\mathrm{\text{−}}\mathrm{SiC}(0001)$ in the graphene Brillouin zone. (b) Simulated STM image of the structure. Wave functions of which energies lie between the Fermi level ($E_F$) and 0.2 eV above $E_F$ are integrated and the image is taken in a plane located at 3 Å above the buffer layer. Bright (dark) regions correspond to a high (low) current in constant-height mode for STM. The $6\sqrt{3}\times 6\sqrt{3}R30°$ periodic lattice vectors are drawn in blue while $6\times 6$ periodic ones in red.

Figure 3

(a) Side view of the atomic structure of graphene on the buffer layer with the $6\sqrt{3}\times 6\sqrt{3}R30°$ periodicity. (b) Simulated STM image of graphene shown in (a). The unit vectors for the $6\sqrt{3}\times 6\sqrt{3}R30°$ periodicity are drawn in blue arrows and those for $6\times 6$ in red. (c) Simulated ARPES spectrum for graphene shown in (a). The bottom of $\sigma$-bands in graphene is shown to be shifted up in energy (pointed by red arrow) compared with that in the buffer layer (blue arrow). The simulated STM image are obtained by the same method as in Fig. 2.

Figure 4

(a) The magnified view of the ARPES spectrum near the Dirac point. (b) Contour plot ($\mathrm{\text{contour spacing}}=0.1\mathrm{eV}$) for the potential generated by the buffer layer and SiC substrate only, drawn on a plane located at 3.35 Å above the buffer layer. The bright (dark) color corresponds to high (low) potential. The hexagonal network (gray lines) for graphene is drawn to guide the eyes. The dark and bright dots represent two sublattices having $\sim 140\mathrm{meV}$ averaged potential difference, respectively. (c) The squared amplitude of wave functions (isosurface of $3.0\times {10}^{-4}/{\AA }^3$) of which energy is located at the upper apex of the energy bands at $K$ [shown in (a)]. The amplitude of the wave function at graphene is denoted in red while the one at the buffer layer in light blue. (d) The squared amplitude of the wave functions whose energies are inside the energy gap at Dirac point (the averaged midgap state). The isosurface value is $3.0\times {10}^{-4}/{\AA }^3$. The red and blue colors for the amplitude follow the same scheme in (c).