  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.
