Provided the electrical properties of electro-burnt graphene junctions can beunderstood and controlled, they have the potential to underpin the developmentof a wide range of future sub-10nm electrical devices. We examine boththeoretically and experimentally the electrical conductance of electro-burntgraphene junctions at the last stages of nanogap formation. We account for theappearance of a counterintuitive increase in electrical conductance just beforethe gap forms. This is a manifestation of room-temperature quantum interferenceand arises from a combination of the semi-metallic band structure of grapheneand a crossover from electrodes with multiple-path connectivity to single-pathconnectivity just prior to breaking. Therefore our results suggest thatconductance enlargement prior to junction rupture is a signal of the formationof electro-burnt junctions, with a pico-scale current path formed from a singlesp2-bond.
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