Coulomb blockade in the quantum-Hall-effect state

It is well known that at low temperature, a small two-dimensional (2D) electron gas shows peaks in the linear conductance at a series of sharply defined values of the external gate voltage. Recently published experimental studies have shown that under a large magnetic field, the value of the gate voltage required to give a peak oscillates as a function of the magnetic field. We explain these oscillations using a simplified model of the island. The model depends on the observation that in the area of each edge state in the island, the electric field is almost completely screened. This prompts us to treat each edge state as a conductor, and to use the Coulomb blockade approach to locate peaks in the conductance of the island. An unusual feature of the system is that the capacitances of the different regions can be controlled by the magnetic field. This, together with a Coulomb blockade within the dot, is what causes the oscillations. We compare our theory with the results of an existing experiment [P. L. McEuen, E. B. Foxman, Jari Kinaret, U. Meirav, M. A. Kastner, N. S. Wingreen, and S. J. Wind, Phys. Rev. B 45, 11 419 (1992)], finding acceptable agreement. A similarity between this system and a single-electron pumping device is noted.