Fig. 3: Curvature-stabilized ABC-TLG.
From: Large-area epitaxial growth of curvature-stabilized ABC trilayer graphene
a AFM topography image showing the corrugated substrate surface, 1D topography profile with a Fourier series fit, and Gaussian fits to the corresponding curvature profiles at corrugation extrema. The AFM image of the substrate was taken after growth and transfer of the graphene film. The measured curvatures were within the resolution of our AFM (see Supplementary Fig. 5). b Schematic of TLG on curved Cu demonstrating how geometric curvature and interlayer-interactions lead to in-plane strain, εκ . Ci denotes graphene where i is the layer index. Substrate and graphene curve lengths are Lsub \(= R_0\theta\) and \(L_i = [R_0 + \left( {4 - i} \right)d_i]\theta\), respectively, such that \(\varepsilon _\kappa \approx (L_i - L_{i + 1})/L_i \approx d_i/R_0 = \kappa d_i\). c Schematics of interlayer dislocation configurations in TLG. \(\bot\) and \(\bot\) denote full and partial dislocations, respectively. The notation is described in the text. d Top views of the \({\mathbf{z}}-{\cal{B}}_2^1{\cal{B}}\). and \({\mathbf{z}}-{\cal{R}}_2^2{\cal{R}}\) interfaces, depicting the origin of CBSS for ABC-TLG; the larger Burgers vector edge component be (normal to the interface) in ABC/ACB domain walls. The three possible (b) directions for each interlayer are shown (arrows); those producing maximum strain relief (largest be) are emphasized. e Computed energies Etot of the states in c vs. maximum curvature κ0 for the zigzag dislocation line direction. Colored regions correspond to different equilibrium states, and vertical gray lines enclose the typical experimental range of κ0 values (the average was \(\kappa _0 \approx 1.5 \times 10^7{\mathrm{m}}^{ - 1}\)). f DFTEM map of ABA (turquoise) and ABC (red-orange) regions onto AFM amplitude image (yellow) of the corresponding growth substrate (see Supplementary Fig. 20 for DFTEM and AFM topography data). White arrows denote maximum curvature lines separating black and yellow regions. AFM amplitude: 348–353 mV. g Measured substrate corrugation peak curvatures and ABC ratios within TLG regions vs. CVD growth time. Error bars are the standard deviation.
