The investigation of the transport properties of single molecules by flowing tunneling currents across extremely narrow gaps is relevant for challenges as diverse as the development of molecular electronics and sequencing of DNA. The achievement of well-defined electrode architectures remains a technical challenge, especially due to the necessity of high precision fabrication processes and the chemical instability of most bulk metals. Here, we illustrate a continuously adjustable tunneling junction between the edges of two twisted graphene sheets. The unique property of the graphene electrodes is that the sheets are rigidly supported all the way to the atomic edge. By analyzing the tunneling current characteristics, we also demonstrate that the spacing across the gap junction can be controllably adjusted. Finally, we demonstrate the transition from the tunneling regime to contact and the formation of an atomic-sized junction between the two edges of graphene.

One-dimensional diffusion of Co adatoms on graphene nanoribbons has been induced and investigated by means of scanning tunnelling microscopy (STM). To this end, the nanoribbons and the Co adatoms have been imaged before and after injecting current pulses into the nanoribbons, with the STM tip in direct contact with the ribbon. We observe current-induced motion of the Co atoms along the nanoribbons, which is approximately described by a distribution expected for a thermally activated one-dimensional random walk. This indicates that the nanoribbons reach temperatures far beyond 100 K, which is well above the temperature of the underlying Au substrate. This model system can be developed further for the study of electromigration at the single-atom level.