Provided the electrical properties of electro-burnt graphene junctions can be understood and controlled, they have the potential to underpin the development of a wide range of future sub-10nm electrical devices. We examine both theoretically and experimentally the electrical conductance of electro-burnt 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 semi-metallic band structure of graphene and a crossover from electrodes with multiple-path connectivity to single-path connectivity just prior to breaking. Therefore our results suggest that conductance enlargement prior to junction rupture is a signal of the formation of electro-burnt junctions, with a pico-scale current path formed from a single sp2-bond.
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