Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co

The appearance of massless Dirac fermions in graphene requires two equivalent carbon sublattices of trigonal shape. While the generation of an effective mass and a band gap at the Dirac point remains an unresolved problem for freestanding extended graphene, it is well established by breaking translational symmetry by confinement and by breaking sublattice symmetry by interaction with a substrate. One of the strongest sublattice-symmetry-breaking interactions with predicted and measured band gaps ranging from 400 meV to more than 3 eV has been attributed to the interfaces of graphene with Ni and Co, which are also promising spin-filter interfaces. Here, we apply angle-resolved photoemission to epitaxial graphene on Ni(111) and Co(0001) to show the presence of intact Dirac cones 2.8 eV below the Fermi level. Our results challenge the common belief that the breaking of sublattice symmetry by a substrate and the opening of the band gap at the Dirac energy are in a straightforward relation. A simple effective model of a biased bilayer structure composed of graphene and a sublattice-symmetry-broken layer, corroborated by density-functional-theory calculations, demonstrates the general validity of our conclusions.

Popular Summary

Graphene is a one-atom-thick sheet of carbon-material wonder, discovered by physicists in 2004 by peeling it off—with Scotch tape—from the banal graphite. Among its many remarkable material properties, one is that its electrons move in it rather like an analogue of massless photons than the massive particles that they actually are. This electronic feature is hallmarked by the so-called Dirac cone in graphene’s electronic structure and is believed to come from a perfect balance between every carbon atom and its closest-neighbor atoms that are arranged into a honeycomb lattice. Should this perfect lattice symmetry be broken, the understanding is that the massless-particle-like characteristic of the electronic movement disappears, or, in other words, that the Dirac cone is broken. This understanding is so well backed both theoretically and experimentally that it has never been questioned—until now. In this paper, we show experimentally that that correlation should not be taken for granted: The electrons in graphene on nickel, where the perfect lattice symmetry is broken, in fact do still travel like massless particles.

In a graphene sheet on nickel, every other carbon atom is strongly bonded to the nickel atom on top of which it sits while its neighboring carbon atoms do not face nickel atoms. This atomic arrangement breaks the original lattice symmetry. So, our observation of still-intact Dirac cones in the graphene on nickel comes as a surprise. The reason for the surprise lies in the fact that the nickel atoms work in two different, compensating ways. On the one hand, they destroy the original perfect lattice symmetry of the graphene; on the other hand, they provide at the same time extra electrons to the graphene sheet—an act that apparently heals the damage caused by the lattice-symmetry breaking and restores the Dirac cones to their full “health.”

Our observation and understanding of the physics underlying the observation add a new piece to the physics of graphene. From a more practical point of view, the fundamental mechanism we have revealed is promising for applications as well where graphene sheets often need to be put on, or supported by, substrates, since the “healing” supply of extra electrons to the graphene comes from a very simple application of a voltage to the graphene layer.

Figure 1

STM evidence for the sublattice symmetry breaking of graphene (a),(b) on Ni(111) and (c),(d) on Co(0001). STM images in (a) and (c) show pronounced threefold symmetry. (b),(d) display structural models of graphene on Ni and Co, respectively, superimposed on the STM data. $A\mathrm{\text{−}}B$ sublattice symmetry breaks due to $\mathcal{A}\mathcal{C}$ stacking, causing different environments for $A$ and $B$ sublattices of graphene (green and red nodes, respectively). Tunneling parameters: $V_t=+2\mathrm{mV}$, $I_t=25\mathrm{nA}$.

Figure 2

ARPES characterization of the gapless dispersion through the $\overline{K}$ point from $\overline{\Gamma }$. Overall band structures of graphene on (a) Ni(111) and on (b) Co(0001) measured along the $\overline{\Gamma M}$ and $\overline{\Gamma K}$ directions of the surface Brillouin zone. The insets on the right-hand side of (a) and (b) emphasize the gapless dispersion of the $\pi$ band at the $\overline{K}$ point.

Figure 3

Full ARPES mapping of the $\pi$ band in graphene on Ni(111) around $\overline{K}$. (a) Constant energy surfaces reveal characteristic triangular contours of the $\pi$ band. The Dirac point (red arrow) is clearly observable at 2.8 eV binding energy. (b) Same as (a) but in isometric representation and with a three-dimensional sketch of the band structure.

Figure 4

Direct observation of intact Dirac cones measured perpendicular to the $\overline{\Gamma K}$ direction. (a),(b) Dirac cone in graphene on Ni(111) measured at $h\nu =62\mathrm{eV}$ (color plot and EDCs). (c),(d) Dirac cone in graphene on Ni(111) sampled at $h\nu =40$ and 80 eV. (e),(f) Intact Dirac cone measured in graphene on Co(0001) at $h\nu =62\mathrm{eV}$ (color plot and EDCs).

Figure 5

Absence of graphene superstructure and multilayer formation. (a) Large-scale STM characterization of graphene on Ni(111) showing no moiré superstructure due to lattice mismatch. (b) The intermediate-scale STM image of graphene on Ni(111) partially intercalated with Au (image contrast is enhanced) reveals a $p(9\times 9)$ moiré above Au islands but no moiré pattern in the graphene on Ni areas. The insets represent LEED images ($E=40\mathrm{eV}$). (c) The electronic structure of graphene decoupled from Ni(111) by intercalation of Au reveals only one Dirac cone, which means that graphene is a monolayer. (d) Control sample [graphene trilayer on Ir(111)] shows characteristic trilayerlike bands after intercalation of Au.

Figure 6

Diminishing band gap in a simplified model for graphene on Ni(111) or Co(0001). The model in geometry (a) corresponds to Eq. (2) and holds near $\overline{K}$. The hopping and on-site energy parameters are assigned typical values: $E_{\mathrm{C}}=-0.3\mathrm{eV}$, $E_s=-1.5\mathrm{eV}$, $E_{\mathrm{V}}=0$, $t_{\mathrm{C}}=3\mathrm{eV}$, $t_s=2\mathrm{eV}$, and $t^{\prime }=0.5\mathrm{eV}$. In (b) and (c), $W$ is set to 0 and $-4\mathrm{V}$, respectively, illustrating the emergence of almost linear dispersion in the case of a large energy difference $eW$.

Figure 7

Dynamic hybridization in the band structure of graphene on Ni(111). The thickness of the lines indicates the band character. (a),(b) Thickness corresponds to the carbon-$p_z$ contribution in sublattice $A$ (directly above Ni, red lines) and sublattice $B$ (no Ni directly underneath, green lines). (c) Thickness corresponds to contributions from the $d$ orbitals of the topmost Ni atom, where $E=(d_{xy},d_{xz},d_{yz},d_{x^2-y^2})$. In all panels, only the majority spin is shown. The minority spin is qualitatively the same.