Imaging confined charge density oscillations on graphite at room temperature

We report the observation of long-range charge density oscillations within the vicinity of superlattice boundaries on graphite at room temperature. These superlattices arise from rotational stacking faults between individual graphene layers on or just below the basal plane. Structural defects in the top graphene layer lead to elastic electron scattering, which is manifest as (i) a $\sqrt{3}$ superstructure at the atomic scale, and (ii) periodic modulations of the superlattice, at much lower spatial frequencies. The measured corrugation of these modulations is energy dependent and decays with increasing distance away from the defects, consistent with previously reported observations on Friedel oscillations in metals. This presents another charge-scattering mechanism limiting conductivity in honeycomb structures having rotational disorder. An understanding of such electronic modifications has important implications for tailoring the transport properties of future carbon electronics based on few-layer graphene.

Figure 1

(a), (b) A 130 × 110 nm${}^2$ area on graphite showing two superlattices (SL) with different periodicity, (left) 11.4 nm and (right) 3.2 nm (−80 mV, 0.2 nA tunneling conditions), and their corresponding two-dimensional (2D) FFT, respectively. The inner hexagonal spots correspond to the larger period SL (left), while the outer hexagonal spots correspond to the smaller period SL (right). Apart from the hexagonal spots, there are 12 spots surrounding the inner hexagonal spots as indicated by the blue arrows and the nested hexagons. These are an indication of additional features hidden within the SL. (c) A 7 × 3 nm${}^2$ area slightly to the left of the defect region indicated by a black box in (a) showing a ($\sqrt{3}$ by $\sqrt{3}$) R30° superstructure propagating off the defect at the atomic scale and its corresponding 2D FFT, taken at specific locations as indicated. The outer hexagonal spots correspond to the graphite lattice, while the inner hexagonal spots (indicated by the arrow), which gradually appear toward the defect (on the right), represent the superstructure, i.e., charge density perturbation at the atomic scale.

Figure 2

The reconstructed image of Fig. 1a on (a) the left of the tear after applying a 2D band-pass filter to the spots corresponding to the modulation of the larger SL (i.e., the spots associated with the nested hexagons). The oscillation patterns (superstructures) are clearly observed as a series of lobes at the superlattice peaks after filtering, and they are disrupted in the vicinity of the vertical defect (boundary), which is just beyond the right-hand edge of the image. (b) The right of the boundary after filtering out the superlattice, illustrating that there are no additional superstructures in this region. (c) An inverted version of Fig. 1a, with no FFT processing, demonstrating that the superstructure features are still clearly visible and are not an artifact of the FFT.

Figure 3

The 57 × 91 nm${}^2$ energy-dependent imaging of the same area in Fig. 2a with inverse FFT band-pass filtering to accentuate the superstructure in the superlattice. The same vertical scale is used in all images. The amplitude of the superstructure decreases gradually, and the features evolve with increasing voltage, demonstrating an energy dependence. The bottom row shows the topography of the same region at the corresponding voltages, also with the same vertical scale in all images (0.25 nm).

Figure 4

(a) A 120 × 110 nm${}^2$ region of the same SL (−100 mV, 0.2 nA) showing a surface line defect as indicated by the arrow, and a boundary between the two SLs. The intensity of the SL remains constant throughout in the presence of the defect. (b) Reconstructed image of (a) after filtering. The dotted line indicates the location of the defect. Note the disruption of the superstructure-like pattern in the vicinity of the boundary.