Single-electron tunnelling in two vertically coupled quantum dots

Electron states in two vertically coupled quantum dots are analysed using an exact-diagonalization method. In the two-electron system, the ground state at zero field is a spin-singlet state, and this state is eventually replaced by spin-triplet states by applying a vertical magnetic field. One of the triplet states is stable under the conditions of very weak coupling and larger asymmetry between the two dots. In the transition from the three- to the four-electron state, we find a parameter region where the tunnelling current is strongly suppressed because of the orthogonality of the quantum states. An isospin selection rule is effective under strong-coupling conditions.