Sketch of energy levels of coupled quantum dots. EM and EN are energies of isolated semimagnetic and non-magnetic dots, respectively. ,j = 1, 2, 3, 4 are the energies of the four states of coupled dots deriving from the spin doublets of lowest orbital states of each quantum dot in the absence of tunneling. Vertical dashed lines indicate dominant couplings of states, which are due to tunneling between levels with like spin states. Arrows indicate spin orientations of the four states. The two spin down levels repel more strongly, which leads to state 3 becoming the ground state at moderate magnetic fields. As discussed in the text, an electric field can be used to change the splitting EM–EN , modifying the coupling of the two quantum dots.
(a) Energies of the upper doublet of spin states vs. external magnetic field. (b) Energies of the lower doublet of spin states vs. external magnetic field. Energies are labeled as in Fig. 1. At magnetic field ∼3.3 T, state 3 becomes the ground state because of the strong repulsion of levels 2 and 3, reversing the order of states in lower doubled compared to Fig. 1.
Energies of four states of coupled quantum dots vs. electric field at external magnetic field slightly above magnetic field 3.3 T corresponding to crossing of Fig. 2(b).
The weights of the wavefunctions of the two lowest energy levels (3 and 4) on the magnetic (M) and non-magnetic quantum, dots as functions of electric field. B = 3.3 T.
Dependence of spin splitting of lowest lying spin doublet vs. electric field for external magnetic fields of 2 T and 6 T.
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