Resonant Tunneling Through Three Quantum Dots with Interdot Repulsion
Arrays of quantum dots have received an increasing amount of interest with the advance of fabrication technologies. At present mostly arrays of 2 coherently coupled dots (double dot) have been studied theoretically and experimentally. In this contribution we present new theoretical results on the resonant transport through a triple quantum dot connected to leads. We assume that the resonant states of each dot are ground states differing by the addition of an extra electron and that a large bias is applied to the leads. In such small structures Coulomb repulsion between electrons in different dots is important. Whereas in a double dot only one charging energy is of importance, in a triple dot we expect that the competition between nearest neighbor and next-nearest neighbor charging energies to affect transport through the structure. The addition energy spectrum of the three dots with interdot charging energies gives rise to many different regimes for resonant tunneling depending on the positioning of the chemical potentials in the leads. For the most interesting regimes we have calculated the stationary resonant current as a function of the tunnel rates to and from the leads and the parameters characterizing the coherent electronic state in the array. In the “free” electron regime interdot charging energies hardly affect transport properties (intradot charging is incorporated) and as many as 3 extra electrons can populate the array. In the Coulomb blockade regime all charging energies large enough to allow at most 1 extra electron in the array. In intermediate regimes a large difference in the finite interdot charging energies can suppress the current through many-electron states with 2 extra electrons by negatively affecting their coherence. This effect is not possible in a double dot.
We employ the density matrix approach, to obtain analytical results in all parameters of our model. These include the coupling to the leads (which has a pronounced influence on the condition for a resonant peak and which is not present in a double dot), the interplay between this coupling and the interdot charging and a possible asymmetry of the array (which affects the coherent couplings and addition energies).