Four interacting electrons in a vertically coupled quantum dots

We studied the ground-state-transition of a vertically coupled four-layer single electron QDs system under a magnetic field by the exact diagonalization of the Hamiltonian matrix. For S=0, the energy spectra of the Dots are calculated as a function of applied magnetic field. We found discontinuous ground-state-transition induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, such a transition does not occur.