Influence of adiabatically transmitted edge channels on single-electron tunneling through a quantum dot

We present a direct comparison of the conductance of a quantum dot in the presence of 2, 1, or 0 adiabatically transmitted edge channels. We observe periodic conductance oscillations as a function of gate voltage for all three cases, and use the Coulomb blockade oscillations observed in the absence of edge channels as a novel electron counter to calibrate the period of the oscillations in the presence of edge channels. We find that the latter set of oscillations cannot be described without invoking Coulomb charging.