Simulation of the Coulomb blockade microscopy of quantum dots

We perform numerical simulation of the Coulomb blockade microscopy on single and double quantum dots (QDs) weakly coupled to the reservoirs of the two-dimensional electron gas. The model describes the screening of the Coulomb charge at the tip of the atomic force microscope by deformation of the electron gas in the QD and in the reservoirs by a self-consistent iteration of DFT equations for the coupled subsystems. We discuss the reaction of the electrons to the tip and the shape of the effective tip potential, which in general becomes short range, strongly dependent on the tip position and asymmetric with a longer tail at the side of the QD. We determine the ground state under influence of the charged probe and obtain charge stability maps of QD as functions of the tip position. We evaluate the charging lines and compare them with the ones obtained for the perturbative conditions for which the charge density is assumed unaffected by the tip.