| We have studied quantum dot arrays of different sizes and shapes both theoretically and experimentally. Theoretically, We proposed that an extended Hubbard model is needed to accurately describe quantum dot arrays. We calculated the addition spectra and conductance for a 2 x 2 quantum dot array. We found that quantum tunneling and capacitive coupling lead to two different effects on the array spectrum so that they are easily told apart.; We further studied ring type quantum dot arrays in the presence of a magnetic field perpendicular to the array. We found that the magnetic field lifts the double degeneracy, and the peak splitting in the addition spectra is periodic in the applied magnetic field with a period equal to one magnetic flux quantum through the ring.; Experimentally, we successfully fabricated a 2 x 2 quantum dot array with an individual tuning gate for each dot. By selectively activating different groups of metal gates, we formed different configurations. Conductance measurements have been successfully conducted for all those systems at dilution refrigerator temperature. In the single quantum dot, we observed periodic Coulomb oscillations. In two dots in series, conductance peak splitting is observed.; In the system of two dots in parallel, we observed peak splitting as we tuned both dots together. Unlike the situation of two dots in series, we observed systematic “high-low, low-high” order of split peaks. Our simulation agrees well with the experimental results, and it indicates that the peak splitting is due to the formation of covalent bonds between the two quantum dots.; In 2 x 2 quantum dot arrays, we observed continuous conductance peak splitting from one peak, to two doublets, and finally to four equally spaced peaks as the coupling between dots is increased. We found that the extended Hubbard model is needed to describe the system realistically, and that capacitive coupling is dominant in the weak coupling regime while quantum tunneling is dominant in the strong coupling regime. The peak splitting we observed indicates the formation of a miniband in the strong coupling regime or what one could call an “artificial molecule”. |
