In Figs. 10, 11, 16(b), 17, 18(b), and 26 we obtained a singlet-triplet transition for the spin splitting between the two lowest energy levels at a critical position of a negatively charged impurity when the impurity is located very close to the quantum dots. Such a transition is incorrect and cannot happen in a two-electron system where the singlet must always be the ground state. In our numerical calculations this transition signals the lack of convergence of the configuration interaction calculations using the quantum dot basis when the repulsive impurity is located very close to the dots, and indicates that this regime is the strong-impurity-coupling regime where the configuration interaction calculations should start from the localized impurity wave function basis rather than the quantum dot basis. These incorrect results were obtained using the quantum dot basis, the nonorthogonal Fock-Darwin states, which, instead, should have been replaced by the hydrogenic impurity basis when the impurity is positioned very close to the coupled two-dot system. All our results showing the singlet-triplet transition should instead be interpreted as the manifestation of the strong-impurity-coupling regime where impurity effects on the coupled quantum dot energy spectra are extremely strong, leading to the possible breakdown of qubit operations. We have now explicitly verified that the singlet is always the ground state of our system at zero magnetic field independent of the impurity location. All the other results in the paper remain unaffected.
展开▼
