Coulomb blockade of tunnelling through compressible rings formed around an antidot: an explanation for $h\mathrm{/}2e$ Aharonov-Bohm oscillations

We consider single-electron tunnelling through antidot states using a Coulomb-blockade model, and give an explanation for h/2e Aharonov-Bohm oscillations, which are observed experimentally when the two spins of the lowest Landau level form bound states. We show that the edge channels may contain compressible regions, and using simple electrostatics, that the resonance through the outer spin states should occur twice per h/e period. An antidot may be a powerful tool for investigating quantum Hall edge states in general, and the interplay of spin and charging effects that occurs in quantum dots.