Transport through double quantum dots

We study transport through two quantum dots in series. Electron-electron interactions are taken into account in the capacitive model with an additional interdot capacitance. The tunneling rates between the dots and the outside reservoirs are assumed to be weak, therefore we treat it perturbatively and derive a master equation. The interdot tunneling is treated in two limits: weak interdot tunneling is included perturbatively, whereas in the opposite limit we assume that there is only one level in the dot in the relevant energy range such that the Hamiltonian of the dots can be diagonalized exactly. We calculate the current through the structure as a function of the two gate voltages. The well-known Coulomb oscillations of a single dot are changed into a characteristic structure of boomerang-like shape. The transport and gate voltages can be time-dependent, and in this case we find that the dependence of the Coulomb oscillations on the two gate voltages allows us to identify which level dominates the transport.