Conductance enlargement in picoscale electroburnt graphene nanojunctions

Provided the electrical properties of electroburnt graphene junctions can be understood and controlled, they have the potential to underpin the development of a wide range of future sub-10-nm electrical devices. We examine both theoretically and experimentally the electrical conductance of electroburnt graphene junctions at the last stages of nanogap formation. We account for the appearance of a counterintuitive increase in electrical conductance just before the gap forms. This is a manifestation of room-temperature quantum interference and arises from a combination of the semimetallic band structure of graphene and a cross-over from electrodes with multiple-path connectivity to single-path connectivity just before breaking. Therefore, our results suggest that conductance enlargement before junction rupture is a signal of the formation of electroburnt junctions, with a picoscale current path formed from a single sp² bond.Graphene nanojunctions are attractive as electrodes for electrical contact to single molecules (1–7), due to their excellent stability and conductivity up to high temperatures and a close match between their Fermi energy and the HOMO (highest occupied molecular orbital) or LUMO (lowest unoccupied molecular orbit) energy levels of organic materials. Graphene electrodes also facilitate electrostatic gating due to their reduced screening compared with more bulky metallic electrodes. Although different strategies for forming nanogaps in graphene such as atomic force microscopy, nanolithography (8), electrical breakdown (9), and mechanical stress (10) have been used, only electroburning delivers the required gap-size control below 10 nm (11–13). This new technology has the potential to overcome the challenges of making stable and reproducible single-molecule junctions with gating capabilities and compatibility with integrated circuit technology (14) and may provide the breakthrough that will enable molecular devices to compete with foreseeable developments in Moore’s law, at least for some niche applications (15–17).One set of such applications is likely to be associated with room-temperature manifestations of quantum interference (QI), which are enabled by the small size of these junctions. If such interference effects could be harnessed in a single-molecule device, this would pave the way toward logic devices with energy consumption lower than the current state-of-the-art. Indirect evidence for such QI in single-molecule mechanically controlled break junctions has been reported recently in a number of papers (18), but direct control of QI has not been possible because electrostatic gating of such devices is difficult. Graphene electroburnt junctions have the potential to deliver direct control of QI in single molecules, but before this can be fully achieved, it is necessary to identify and differentiate intrinsic manifestations of room-temperature QI in the bare junctions, without molecules. In the present paper, we account for one such manifestation, which is a ubiquitous feature in the fabrication of picoscale gaps for molecular devices, namely an unexpected increase in the conductance before the formation of a tunnel gap.Only a few groups in the world have been able to implement electroburning method to form nanogap-size junctions. In a recent study of electroburnt graphene junctions, Barreiro et al. (19) used real-time in situ transmission electron microscopy (TEM) to investigate this conductance enlargement in the last moment of gap formation and ruled out the effects of both extra edge scattering and impurities, which reduce the current density near breaking. Also, they showed that the graphene junctions can be free of contaminants before the formation of the nanogap. Having eliminated these effects, they suggested that the enlargement may arise from the formation of the seamless graphene bilayers. Here we show that the conductance enlargement occurs in monolayer graphene, which rules out an explanation based on bilayers. Moreover, we have observed the enlargement in a large number of nominally identical graphene devices and therefore we can rule out the possibility of device- or flake-specific features in the electroburning process. An alternative explanation was proposed by Lu et al. (20), who observed the enlargement in few-layer graphene nanoconstrictions fabricated using TEM. They attributed the enlargement to an improvement in the quality of few-layer graphene due to current annealing, which was simply ruled out by our experiments on electroburnt single-layer graphene. They also attributed this to the reduction of the edge scattering due to the orientation of the edges (i.e., zigzag edges). However, such edge effects have been ruled out by the TEM images of Barreiro et al. (19). Therefore, although this enlargement appears to be a common feature of graphene nanojunctions, so far the origin of the increase remains unexplained.In what follows, our aim is to demonstrate that such conductance enlargement is a universal feature of electroburnt graphene junctions and arises from QI at the moment of breaking. Graphene provides an ideal platform for studying room-temperature QI effects (21) because, as well as being a suitable material for contacting single molecules, it can serve as a natural 2D grid of interfering pathways. By electroburning a graphene junction to the point where only a few carbon bonds connect the left and right electrodes, one can study the effect of QI in ring- and chain-like structures that are covalently bonded to the electrodes. In this paper, we perform feedback-controlled electroburning on single-layer graphene nanojunctions and confirm that there is an increase in conductance immediately before the formation of the tunnel junction. Transport calculations for a variety of different atomic configurations using the nonequilibrium Green’s function (NEGF) method coupled to density functional theory (DFT) show a similar behavior. To elucidate the origin of the effect, we provide a model for the observed increase in the conductance based on the transition from multipath connectivity to single-path connectivity, in close analogy to an optical double-slit experiment. The model suggests that the conductance increase is likely to occur whenever junctions are formed from any sp²-bonded material.