Identification of graphite with perfect rhombohedral stacking by electronic Raman scattering

Abstract

Rhombohedral graphite (RG) shows strong correlations in its topological flat band and is pivotal for exploring emergent, correlated electronic phenomena. One key advantage is the enhancement of electronic interactions with the increase in the number of rhombohedrally stacked graphene layers. Increasing thickness also leads to an exponential increase in the number of stacking faults, necessitating a precise method to identify flawless rhombohedral stacking. Overcoming this challenge is difficult because the established technique for stacking sequence identification, based on the Raman 2D peak, fails in thick RG samples. We demonstrate that the strong layer dependence of the band structure can be harnessed to identify RG without stacking faults, or alternatively, to detect their presence. For thicknesses ranging from 3 to 12 layers, we show that each perfect RG structure presents distinctive peak positions in electronic Raman scattering (ERS). This measurement can be carried out using a conventional confocal Raman spectrometer at room temperature, using visible excitation wavelengths. Consequently, this overcomes the identification challenge by providing a simple and fast optical measurement technique, thereby helping to establish RG as a platform for studying strong correlations in one of the simplest crystals possible.

Figures (6)

• Figure 1: Similarity of 2D peak shapes for thick RG.(a) Example Raman spectra of the 2D peak, from areas of a graphite flake with predominant rhombohedral stacking. The spectra are selected from areas with 7, 8 and 10 graphene layers. Dashed lines show the lower and upper Raman shift values, used for calculating the integrated intensity ratio map shown in (b). Numbers to the right of the spectra are the integrated intensity ratio of the measurements. Errors stem from the local variability within the map in (b). (b) Map of the integrated Raman intensity in the range 2675 to 2705 cm$^{-1}$ divided by the integrated intensity in the range 2705 to 2735 cm$^{-1}$, as introduced by Yang et al Yang2019-yx. Larger values correspond to more prominent rhombohedral stacking. (c) Optical microscopy image of the flake. Positions of selected spectra shown in (a), marked by "+" signs of corresponding colour. Raman spectra are measured, using 532 nm excitation.
• Figure 2: Raman spectra of rhombohedral graphite.(a) Optical microscopy image of a graphite flake. Red numbers indicate the number of graphene layers. Black rectangles show the positions of the AFM images in (b) and (c). (b) AFM (tapping mode) topography image of the flake in (a). The flake has a single graphene layer protrusion, which was used as the reference for AFM height measurements. The single layer nature of the flake is shown by the green Raman spectrum in the lower inset, measured at the position shown by the green "x". Right inset: height section of the flake along the red line. The flake is $2.32$ nm thick, relative to the bottom graphene, meaning 8 graphene layers in total. (c) AFM (tapping mode) topography image of the single layer step in the middle of the flake. The hexagonal - rhombohedral domain wall is marked by the black arrows. Lower inset shows the height histogram of the image. (d) Integrated intensity ratio of the 2D peak. (e) Raman spectra averaged in the areas marked by correspondingly coloured dashed outlines in (d), each spectrum is an average of 50 to 80 spectra, with an individual integration time of 2 s. Top panel: spectra are offset for clarity. Bottom panel: same spectra as in the top panel, showing the background signal. Electronic Raman scattering (ERS) peaks marked by black arrows. Raman spectra are measured, using 488 nm excitation.
• Figure 3: Extracting the ERS signal.(a) Left: ab initio band structure around the K point of 7 layer RG. Energy is with respect to the Fermi level ($E_{\mathrm{F}}$). Right: density of states (DOS) at selected RG thicknesses. The transitions between the DOS peaks, which result in the ERS signal, are shown by arrows. (b) Raman spectra of the 7 and 8 layer regions in Fig. \ref{['fig:id']}, measured using crossed polarization. Arrows mark the ERS signal, associated with the transitions between the DOS peaks. (c) Example of extracting the ERS signal. This is achieved by subtracting the spectrum measured with parallel polarization from the one acquired using the crossed polarizer configuration. Prior to subtraction, both spectra are normalized to the 4300 cm$^{-1}$ peak. Gaussian fits applied to the resultant ERS signals are also displayed. Raman spectra are measured, using 488 nm excitation, integration time for each spectrum is 20 s.
• Figure 4: Layer number dependence of ERS peaks in RG.(a) Difference of crossed/parallel spectra for graphene layer numbers between 3 and 12. Positions of the ERS peaks are shown by red and green triangles. From 3 to 8 layers, the spectra are normalized to the 2D + G mode at 4300 cm$^{-1}$. For 9 layers, the 2D peak and for 10, 11 and 12 layers the 2D' (3247 cm$^{-1}$) peak was used for normalization. Spectra are offset and scaled along the y axis for better visibility. (b) ERS peak positions for the first and second transitions. Blue crosses show the calculated ERS peak positions from refs Garcia-Ruiz2019-dpMcEllistrim2023-op. Error bars that are not shown are smaller than the symbols (40 cm$^{-1}$). (c) Direct measurement of the DOS, for 3 (bottom) and 4 layer (top) RG by scanning tunnelling microscopy (STM). The energy gap associated with the $-1 \rightarrow +1$ transitions is shown by grey arrows. (d) Comparison of the direct DOS peak energy separation (from STM) and the ERS signal measured on 3 and 4 layers. Red data points denote the average from measurements across multiple flakes: four for trilayer and three for tetralayer. Error bars for Raman measurements represent weighted estimated errors, while STM error bars are based on the standard deviation of energy separation values across the sample. Raman spectra are measured, using 488 nm excitation. STM data was measured at a temperature of 9 K.
• Figure 5: Mapping the ERS across a flake.(a) Intensity of the ERS signal across the 7 and 8 layer flake. Top: selected spectra, where the phonon peaks are removed as shown in Fig. \ref{['fig:ers_extracting']}c. Coloured arrows show the Raman shift, for which the ERS intensity is plotted in the bottom panel. Bottom: maps of the ERS intensity for the $-1 \rightarrow +1$ transition for the 8 (blue) and 7 layer (red) ERS peak. Black numbers show the number of graphene layers in the region. (b) ERS peak position in cm$^{-1}$ for the 7 and 8 layer areas, as determined by Gaussian fitting (see Fig. \ref{['fig:ers_extracting']}c). The whole flake is marked as the grey area. Top: histograms of the peak positions, black bars show the size of the standard deviation (7 layer: 6 cm$^{-1}$, 8 layer: 2.9 cm$^{-1}$). Raman spectra are measured, using 488 nm excitation.