Coulomb Blockade in a Quantum Dot Coupled Strongly to a Lead

We study theoretically a quantum dot in the quantum Hall regime that is strongly coupled to a single lead via a point contact. We find that even when the transmission through the point contact is perfect, important features of the Coulomb blockade persist. In particular, the tunneling into the dot via a second weakly coupled lead is suppressed, and shows features which can be ascribed to elastic or inelastic cotunneling through the dot. When there is weak backscattering at the point contact, both the tunneling conductance and the differential capacitance are predicted to oscillate as a function of gate voltage. We point out that the dimensionless ratio $\xi$ between the fractional oscillations in $G$ and $C$ is an intrinsic property of the dot, which, in principle, can be measured. We compute $\xi$ within two models of electron-electron interactions. In addition, we discuss the role of additional channels.