Edge states of moiré structures in graphite

We address the origin of beadlike edge states observed by scanning tunneling microscopy (STM) in moiré patterns of graphite. Low-bias STM measurements indicate these edge states are centered around $AB$ stacking sites, contrary to the common assumption of them being at $AA$ sites. This shift in the beads intensity with respect to the bulk moiré pattern has been corroborated by a tight-binding calculation of the edge states in bilayer flakes. Our results are valid not only for graphite, but also for few-layer graphene where these states have also been recently observed.

Figure 1

Typical STM image of a moiré superlattice in HOPG collected with a bias voltage of 100 mV. Both edge states and bulk moiré patterns are clearly observed. (a) Wide overview of the surface; (b) detailed section of the edge where it is clear that the edge states do not follow the symmetry of the superlattice; (c) detailed view of the bulk moiré pattern, used to estimate the size of the supercell; (d) detailed view of the coexistence of the triangular atomic unit cell of graphite and the brighter moiré intensity induced by the layer rotation.

Figure 2

STM (LDOS) simulation of edge states. (a) STM line profile along the left edge of the terrace. In dashed blue we indicate the profile for energies $E$ in the range $E_F-100\mathrm{meV}<E<E_F$ and in solid green for $E_F-500\mathrm{meV}<E<E_F$. (b) Simulation of the STM topographic profile for a tip voltage of 100 mV. The line profile depicted in (a) was measured along the dashed line close to the edge of the top flake.

Figure 3

Band structures of graphene bilayer nanoribbons with stacking (a) $AB$ and (b) $AA$. The width of the ribbons is equal to eight dimer chains in both cases.

Figure 4

STM (LDOS) simulation of a wide flake over graphene with energies $E$ in the range $E_F-500\mathrm{meV}<E<E_F$. (a) STM line profile along the center of the flake. (b) The dashed line shows the direction of the line profile in (a). Coexistence of edge states and bulk moiré pattern can be observed.