Hexagonal-boron nitride substrates for electroburnt graphene nanojunctions

• Geometrical structures at the last stages of nanogap formation are obtained.
• The electrical conductance of such structures is predicted to be only marginally affected by the presence of hBN.
• The junctions exhibit a counterintuitive increase in electrical conductance just before the gap forms.

We examine the effect of a hexagonal boron nitride (hBN) substrate on electron transport through graphene nanojunctions just before gap formation. Junctions in vacuum and on hBN are formed using classical molecular dynamics to create initial structures, followed by relaxation using density functional theory. We find that the hBN only slightly reduces the current through the junctions at low biases. Furthermore due to quantum interference at the last moments of breaking, the current though a single carbon filament spanning the gap is found to be higher than the current through two filaments spanning the gap in parallel. This feature is present both in the presence of absence of hBN.