Dirac Fermions in Strongly Bound Graphene Systems

It is highly desirable to integrate graphene into existing semiconductor technology, where the combined system is thermodynamically stable yet maintain a Dirac cone at the Fermi level. First-principles calculations reveal that a certain transition metal (TM) intercalated $\mathrm{\text{graphene}}/\mathrm{SiC}(0001)$, such as the strongly bound graphene on SiC with Mn intercalation, could be such a system. Different from freestanding graphene, the hybridization between graphene and $\mathrm{Mn}/\mathrm{SiC}$ leads to the formation of a dispersive Dirac cone of primarily TM $d$ characters. The corresponding Dirac spectrum is still isotropic, and the transport behavior is nearly identical to that of freestanding graphene for a bias as large as 0.6 V, except that the Fermi velocity is half that of graphene. A simple model Hamiltonian is developed to qualitatively account for the physics of the transfer of the Dirac cone from a dispersive system (e.g., graphene) to an originally nondispersive system (e.g., TM).

Figure 1

Top view of the optimized geometries of the $\mathrm{G}/i\mathrm{\text{−}}\mathrm{TM}/\mathrm{SiC}$ systems, (a) Sc, Ti, V, Cr, Mn, and Fe, (b) Co, and (c) Ni. (d) Side view of the geometry corresponding to (a). Yellow (large, gray), gray, and white balls are Si, C, and H, respectively, while others are TM elements. For clarity, graphene is shown as hexagonal mesh. Rhombus denotes the supercell.

Figure 2

Band structures of the $\mathrm{G}/i\mathrm{\text{−}}\mathrm{TM}/\mathrm{SiC}$ systems. Bands having a linear (or nearly linear) dispersion around the $K$ point and near the $E_F$ are highlighted by magenta except for spin-polarized $\mathrm{G}/i\mathrm{\text{−}}\mathrm{Cr}/\mathrm{SiC}$ for which black solid lines denote majority-spin states and green dashed lines denote minority-spin states. Fermi levels are set to zero. For $\mathrm{G}/i\mathrm{\text{−}}\mathrm{V}/\mathrm{SiC}$, although the two bands near the Fermi level also cross each other at the $\Gamma$ point, the dispersion is largely parabolic rather than being linear.

Figure 3

(a) Schematic drawing of the hybridization between Mn orbitals and the three dangling-bond orbitals of surface Si in $\mathrm{Mn}/\mathrm{SiC}$. Each arrow denotes one electron with up or down spin, while each black dot denotes two (spin-degenerate) electrons. (b) Local density of states of $\mathrm{G}/i\mathrm{\text{−}}\mathrm{Mn}/\mathrm{SiC}$. Zero is the Fermi level. (c) Schematic drawing of the hybridization between the Dirac cone of $\mathrm{Mn}/\mathrm{SiC}$ and that of graphene: left is before and right is after.

Figure 4

(a) Band structure around the Dirac point for $\mathrm{G}/i\mathrm{\text{−}}\mathrm{Mn}/\mathrm{SiC}$. Left: three-dimensional view and right: constant energy contours. Color represents vertical distance from zero energy surface. (b) The $I\mathrm{\text{−}}V$ curves for 11-AGNR ($=$ armchair graphene nanoribbon with 11 dimer rows) with and without the $\mathrm{Mn}/\mathrm{SiC}$ support. Inset shows the atomic structure for transport calculations.