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Two dimensional materials are usually envisioned as flat, truly 2D layers. However out-of-plane corrugations are inevitably present in these materials. In this manuscript, we show that graphene flakes encapsulated between insulating crystals (hBN, WSe2), although having large mobilities, surprisingly contain out-of-plane corrugations. The height fluctuations of these corrugations are revealed using weak localization measurements in the presence of a static in-plane magnetic field. Due to the random out-of-plane corrugations, the in-plane magnetic field results in a random out-of-plane component to the local graphene plane, which leads to a substantial decrease of the phase coherence time. Atomic force microscope measurements also confirm a long range height modulation present in these crystals. Our results suggest that phase coherent transport experiments relying on purely in-plane magnetic fields in van der Waals heterostructures have to be taken with serious care.

We investigate the quality of hydrogen plasma defined graphene edges by Raman spectroscopy, atomic resolution AFM and low temperature electronic transport measurements. The exposure of graphite samples to a remote hydrogen plasma leads to the formation of hexagonal shaped etch pits, reflecting the anisotropy of the etch. Atomic resolution AFM reveals that the sides of these hexagons are oriented along the zigzag direction of the graphite crystal lattice and the absence of the D-peak in the Raman spectrum indicates that the edges are high quality zigzag edges. In a second step of the experiment, we investigate hexagon edges created in single layer graphene on hexagonal boron nitride and find a substantial D-peak intensity. Polarization dependent Raman measurements reveal that hydrogen plasma defined edges consist of a mixture of zigzag and armchair segments. Furthermore, electronic transport measurements were performed on hydrogen plasma defined graphene nanoribbons which indicate a high quality of the bulk but a relatively low edge quality, in agreement with the Raman data. These findings are supported by tight-binding transport simulations. Hence, further optimization of the hydrogen plasma etching technique is required to obtain pure crystalline graphene edges., Comment: 10 pages, 7 figures

We investigate the etching of a pure hydrogen plasma on graphite samples and graphene flakes on SiO$_2$ and hexagonal Boron-Nitride (hBN) substrates. The pressure and distance dependence of the graphite exposure experiments reveals the existence of two distinct plasma regimes: the direct and the remote plasma regime. Graphite surfaces exposed directly to the hydrogen plasma exhibit numerous etch pits of various size and depth, indicating continuous defect creation throughout the etching process. In contrast, anisotropic etching forming regular and symmetric hexagons starting only from preexisting defects and edges is seen in the remote plasma regime, where the sample is located downstream, outside of the glowing plasma. This regime is possible in a narrow window of parameters where essentially all ions have already recombined, yet a flux of H-radicals performing anisotropic etching is still present. At the required process pressures, the radicals can recombine only on surfaces, not in the gas itself. Thus, the tube material needs to exhibit a sufficiently low H radical recombination coefficient, such a found for quartz or pyrex. In the remote regime, we investigate the etching of single layer and bilayer graphene on SiO$_2$ and hBN substrates. We find isotropic etching for single layer graphene on SiO$_2$, whereas we observe highly anisotropic etching for graphene on a hBN substrate. For bilayer graphene, anisotropic etching is observed on both substrates. Finally, we demonstrate the use of artificial defects to create well defined graphene nanostructures with clean crystallographic edges., Comment: 7 pages, 4 color figures