Structurally driven one-dimensional electron confinement in sub-5-nm graphene nanowrinkles

Graphene-based carbon materials such as fullerenes, carbon nanotubes, and graphenes have distinct and unique electronic properties that depend on their dimensionality and geometric structures. Graphene wrinkles with pseudo one-dimensional structures have been observed in a graphene sheet. However, their one-dimensional electronic properties have never been observed because of their large widths. Here we report the unique electronic structure of graphene nanowrinkles in a graphene sheet grown on Ni(111), the width of which was small enough to cause one-dimensional electron confinement. Use of spatially resolved, scanning tunnelling spectroscopy revealed bandgap opening and a one-dimensional van Hove singularity in the graphene nanowrinkles, as well as the chemical potential distribution across the graphene nanowrinkles. This observation allows us to realize a metallic-semiconducting-metallic junction in a single graphene sheet. Our demonstration of one-dimensional electron confinement in graphene provides the novel possibility of controlling its electronic properties not by chemical modification but by ‘mechanical structuring'.

Outside the EG, line structures of Ni 2 C and many contaminants were confirmed Then, |M| could be calculated as 3.31 (for R= 3.68or 0.54 nm (for R= 26.7 by using Supplementary Equation 2. We therefore concluded that the Moiré pattern in Supplementary   Fig. 2 had R3.68  orientation.

Supplementary Note 2. Mechanism of formation of GNWs
As shown in Fig. 2a  Our results can also be explained by the "step-induced wrinkle" mechanism, because atomic-scale steps exist intrinsically on the surface. During the cooling process in EG synthesis, the difference in thermal expansion between the EG and Ni surface induces a compressive strain in the EG ( Supplementary Fig. 4 (left)). Compared to the EG on the flat terrace of the Ni substrate, the EG at the step edge does not interact strongly with the substrate; therefore, due to the strain, it can be folded only on the step edge ( Supplementary Fig. 4 (right)). In general, graphene wrinkles on the terrace of an underlying substrate have been simply understood to result from substrate contraction due to differences of thermal expansion. However, most of the GNWs, even on the terrace, emerged from the kink of the step edge. This process is usually not observed on a bare Ni(111) surface.
Although the mechanism of formation of GNWs on the Ni(111) terrace region has yet to be completely understood, we argue that step edges of Ni(111) play a critical role, even for the GNWs on the terrace region.

Supplementary Note 3. Estimation of arc lengths from widths and heights of GNWs -Method 1. Estimation with height and width value base on the assumption of a circular shape
To compare our results with the energy gap in SWCNTs and graphene nanoribbons, we estimated the arc length (l) of the GNWs with height (h) and width (w) values measured by STM, because the length for electron confinement in the GNW was comparable to the circumference of SWCNTs and widths of graphene nanoribbons. For the calculation, we assumed that the GNW was part of a circle ( Supplementary Fig. 6). By using Supplementary   Equation 3 and a simple trigonometric function, we calculated the arc length for the GNWs (Fig. 3a). The E g s with respect to the calculated arc length are plotted in Fig. 3b by two methods is confirmed as -1 ~ 8 %, but in the cases of GNW ii and GNW iv having higher error values (5.6 % and 7.6 %), their arc lengths were overestimated due to the atomic protrusion or the noise on the height profile. Supplementary Figs. 8a,b show the height profiles of GNWs ii and v, respectively. While GWN b has a smooth height profile, the GNW e has more rough height profile, which might be originated not only by the atomic protrusion but also the noise during the measurement. This implies that the direct measurement from the experimentally measured height profile can provide a more relevant quantity, but some cases can provide an overestimated quantity such as GNWs ii and v. Nevertheless, we confirmed that the arc lengths obtained by our method (Method 1) based on the assumption that the GNW arc shape is part of a circle c is comparable with the experimental values obtained by the method 2, except some specific cases having higher roughness on their height profiles.
Therefore, we believe that our assumption can be conveniently used for estimating the GNW arc length.