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 sha rply defined values of the external gate voltage. Recently published e xperimental studies have shown that under a large magnetic field, the value of the gate voltage required to give a peak oscillates as a func tion of the magnetic field. We explain these oscillations using a simp lified 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 al most 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 th e magnetic field. This, together with a Coulomb blockade within the do t, is what causes the oscillations. We compare our theory with the res ults of an existing experiment (P. L. McEuen, E. B. Forman, Jari Kinar et, U. Meirav, M. A. Kastner, N. S. Wingreen, and S. J. Wind [Phys. Re v. B 45, 11419 (1992)]) finding acceptable agreement. A similarity bet ween this system and a single-electron pumping device is noted.