▎ 摘　　要

In a Josephson junction between two exciton condensates, the tunneling of charge-neutral electron-hole pairs has gained primary attention in the form of a supercurrent, which otherwise is challenging to detect experimentally. Here we design excitonic Josephson junctions based on graphene heterostructures that allow us to selectively sustain charge-neutral or charged supercurrent, offering unprecedented opportunities for revealing exotic physics of exciton condensates. In our schemes, each exciton condensate consists of a graphene monolayer vertically coupled with another graphene monolayer (GML), bilayer, or trilayer, shown to have characteristically different quantum phase transition temperatures. When two such identical condensates are connected, a neutral supercurrent always dominates within the GML/GML scheme, while in the other two schemes, a carrier-density induced transition can take place between the neutral and charged supercurrents. More strikingly, in the charged regime, both the electron or hole dominance and the DC or AC nature can be tuned by the chemical potential differences of the junction. These findings are also expected to be applicable to excitonic Josephson junctions beyond the graphene-based architecture.