Aharonov-Bohm conductance oscillations and current equilibration in local n - p junctions in graphene

We consider a small p-type island defined within n-type graphene nanoribbon induced by potential of a floating electrode. In the quantum Hall conditions the island supports persistent currents localized at the $n-p$ junction. When coupled to the graphene edge the island acts as an Aharonov-Bohm interferometer. We evaluate the electrostatic potential induced by the floating gate within the ribbon near the charge neutrality point and consider equilibration of the currents at both sides of the junction. The incoherent equilibration is introduced by the virtual probes technique. We describe the evolution of the coherent Aharonov-Bohm conductance oscillations to the quantum Hall fractional plateaus due to the current equilibration.