Designing exciton-condensate Josephson junction in graphene heterostructure

Exciton condensation have been robustly realized in several 2D-material heterostructures, specifically graphene quantum hall bilayers. This work proposes a realistic setup of exciton-condensate Josephson junction and a measurement ansatz in such systems.The junction mimics the S-I-S structure of the ordinary Josephson junction, where the insulating barrier is a layer-polarized quantum Hall state controlled by external gating. We estimate the strength of Josephson coupling as a function of junction width, which reveals its high range of tunability. Finally, we propose a capacitive measurement ansatz of the Josephson frequency.