Resonant tunneling in the fractional quantum hall effect: Superperiods and braiding statistics

We study theoretically resonant tunneling of composite fermions through their quasibound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These have possible relevance to a recent experimental study, and reveal many subtleties involved in deducing fractional braiding statistics.