Multiply folded graphene

The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material, folding may transform it to complex shapes with new and distinct properties. Here, we present experimental results that folded structures in graphene, termed grafold, exist, and their formations can be controlled by introducing anisotropic surface curvature during graphene synthesis or transfer processes. Using pseudopotential-density-functional-theory calculations, we also show that double folding modifies the electronic band structure of graphene. Furthermore, we demonstrate the intercalation of ${\mathrm{C}}_{60}$ into the grafolds. Intercalation or functionalization of the chemically reactive folds further expands grafold's mechanical, chemical, optical, and electronic diversity.

Figure 1

Various multiple folding structures of graphene. (a) Planar figure of graphene before double folding. The dotted blue lines are folding lines, whose directions are measured relative to the direction of the ${\mathrm{a⃗}}_1-{\mathrm{a⃗}}_2$ vector in the graphene lattice. (b) Double folding of single layer graphene produces local triple-layer graphene. Upper, middle, and bottom graphene layers are shown in blue, red, and yellow, respectively. (c) A planar view of graphene before parallel double-folding (pleat folding). The translational vector between the two folding lines can be indexed as $n{\mathrm{a⃗}}_1+m{\mathrm{a⃗}}_2$. (d) Top view of a folding structure with $\theta ={11}^{°}$. Top and bottom graphene layers have the same rotational direction. (e)–(g) Top views of folding structures with $\theta =0^{°}$, where foldings occur along the zigzag lattice direction of graphene. The layer stacking can vary depending on where the folding lines occur. (e) AAA stacking of the folding structure with $n=m=4\frac{1}{2}$. (f) ABA stacking with $n=m=4\frac{1}{2}$. (g) ABC stacking with $n=m=4\frac{2}{3}$. (h) Various complex folding structures with quadruple foldings, including a box pleat (left). (i) Periodic double folding superstructure. Folds can be used as a local intercalation platform, and highly curved edges can be functionalized with foreign materials.

Figure 2

TEM and diffraction analysis of double folding structures. (a) TEM image of a ribbonlike folding structure in suspended graphene. (b) HAADF (high-angle annular dark field) STEM image of a graphene sheet with a folding structure. Circles denote different locations 1–7 for diffraction acquisition using a nanoparallel electron beam (NPEB). The NPEP has a diameter of 45 nm. (c)–(e) Series of diffraction patterns across the folding structure. (c) Diffraction pattern at location 1. (d) Diffraction pattern at location 4, at the folding. Inset shows a zoom-in image of the (0-220) $A$ spot, which shows the splitting of two spots with a very small rotation angle of 0.4°. (e) Diffraction pattern at the location 7. (f) Diffraction spot intensity ($A$ spot, $B$ spot, their sum, and their difference) variations at different locations.

Figure 3

SEM, AFM, and STEM images of folds in CVD graphene. (a) SEM images of CVD graphene transfered to a silicon oxide/silicon substrate. Folds appear dark relative to monolayer graphene. (b) HAADF STEM image of CVD graphene transfered to a Quantifoil holey carbon TEM grid. The white background is the region of the amorphous carbon film and the dashed lines are a guide to the eyes for folds in graphene. (c) AFM scan of graphene fold in CVD graphene transfered to silicon oxide/silicon substrate. (d) Top: The height profile of the folding structure along the dotted line in c. Bottom: Proposed folding structure (double folding) from the AFM data. (e) Top: AFM scan of multiple folding structure in graphene. The white dotted line is used for the height profile scan. Middle: The height profile of the folding structure. The height difference (0.7 nm) of observed steps is consistent with the thickness of double layer graphene. Bottom: Proposed folding structure (quadruple folding) from the AFM data.

Figure 4

Atomic resolution TEM image of a pleat folding structure. (a) A double folding structure with parallel folding lines with $\theta ={27}^{°}$. To the left and right of the folding structure is monolayer graphene. The folding edges are overlaid with blue dotted lines. (b) Fast Fourier transform (FFT) of (a), which shows two sets of hexagonal patterns. The circled set of hexagonal pattern (red) is from middle layers. The blue dotted line is drawn to be parallel to the folding lines. The hexagonal set marked by blue arrows is from top and bottom graphene layers, which have the same lattice directions after folding.

Figure 5

Theoretical calculation of double folding structures in graphene. (a) Model of the pleat folding structure of $\theta =0^{°}$ that has been relaxed. The fold is periodic into the page, although only a finite width is shown here for clarity. (b) Electronic band structure of the pleat folding along the direction of the fold. The system is semimetallic with a slight indirect overlap between the occupied and unoccupied states. (c) Calculated local density of states integrated for the occupied states from 0.1 eV below $E_F$ to $E_F$ for a narrow double folding with a triple layer region of length ∼1 nm. The shown isosurface is 10% of the maximum value and shows that the occupied states near the Fermi level are localized to the region near the fold.

Figure 6

Controlled folding formations in graphene: comparison of graphene folding formations from regular and patterned copper substrates. (a) Histogram of angle-dependent fold formation frequency in graphene grown on unpatterned copper foil. (b) Histogram of angle-dependent folded area in folds in graphene grown on unpatterned regular copper foil. (c) Schematic process of directional control of folding formations in graphene during synthesis. A copper substrate with patterned etched trenches is used for CVD graphene growth. After transferring the graphene to other substrates, foldings are more frequently aligned with the patterned direction. (d) and (e) Graphene synthesized using the patterned copper substrate and transferred to a Quantifoil holey carbon TEM grids. Aligned folding formations are observed. $\varphi =0^{°}$ is the pattern direction in the copper substrate. (f) and (g) Histogram of angle-dependent fold formation frequency and folded area in graphene grown on etched line trenches of copper foil. The angle at zero degrees is the direction of the patterns.

Figure 7

Proposal for controlled placement of grafold. (a) Schematic process of controlled placement of folds in graphene. Graphene is transferred onto a substrate which has patterned metal features. After underetching of the metal features, the graphene collapses and may fold along these prepatterned regions. (b) SEM image of graphene draped over a copper metal pattern on a silicon substrate. (c) SEM image of the same region after the copper is underetched. The image is suggestive of graphene folding aligned with the removed copper structure.

Figure 8

Intercalation of C60 into a single fold in graphene. (a) TEM image of a graphene edge fold with intercalated ${\mathrm{C}}_{60}$. Along the straight fold edge, ${\mathrm{C}}_{60}$ are closely packed forming a single chain of ${\mathrm{C}}_{60}$. (b) Schematic view of the fold structure with local ${\mathrm{C}}_{60}$ intercalation.

Figure 9

Schematic of indexing of a pleat folding structure. (a) Assignment of an axis of interest in the folding structure. There are three points of interest which are intersected by the blue dashed line in the three stacked graphene layers. (b) Top view of the folding structure shown in Fig. 9a. An ABC-stacking relation can be identified in the flat region and the points of interest are marked by the blue dot. (c) Unfolding the structure to obtain a flat graphene sheet and finding the translational vectors connecting the three points of interest to index the folding lines (blue dashed lines). In the folding structure shown in the schematic, the indexing is $n=m=14\frac{2}{3}$.

Figure 10

Calculated band structures of shifted bilayer graphene. (a)–(d), Calculated band structures along the $M$→$K$→Γ direction for two layers of graphene, (top) with corresponding atomic structures, (bottom) having different relative shifts in the armchair direction. (a) and (c) are for $\mathit{AA}$ and $\mathit{AB}$ stacking, respectively, while (b) and (d) are intermediate stackings. In (a), two pairs of bands cross at $E_F$ away from the $K$ point and have linear dispersion. In (c), conduction and valence bands touch at $E_F$ at the $K$ point and have quadratic dispersion. The intermediate case (b) shows a gap, with band extrema away from the $K$ point. In (d), a band crosses $E_F$ at two points away from the $K$ point.