Exchange energy tuned by asymmetry in artificial molecules

Laterally coupled asymmetric quantum dots occupied by two electrons are studied using the exact diagonalization approach. It is shown that the asymmetry enhances the exchange energy, i.e., the triplet-singlet energy difference for finite magnetic fields. At high magnetic field, electrons enter the deepest dot more easily if they have parallel spins.

Figure 1

Confinement potential (dotted line) and singlet (solid line) and triplet (dashed line) charge density plotted in arbitrary units at $y=0$ axis for $V_r=25\mathrm{meV}$ and (a) $V_l=25\mathrm{meV}$ and $B=0$, (b) $V_l=32\mathrm{meV}$ and $B=0$, (c) $V_l=25\mathrm{meV}$ and $B=10\mathrm{T}$, (d) $V_l=32\mathrm{meV}$ and $B=6\mathrm{T}$.

Figure 2

(a) Charge accumulated at left of the origin for $d=52\mathrm{nm}$ and $d=60\mathrm{nm}$ in the singlet (solid lines) and triplet (dotted lines) states as function of the depth of the left quantum well $V_l$. Data for $d=52\mathrm{nm}$ are marked with squares. (b) Probabilities that both electrons are on the same side of the origin for the singlet (solid lines) and triplet (dotted lines) states for $d=52\mathrm{nm}$. (c) Singlet-triplet energy difference as function of $V_l$. The values for $d=48$, 52 and 60 nm are plotted with dashed, solid and dotted lines, respectively.

Figure 3

Probability that both electrons are on the same side of the origin for singlets (solid lines) and triplets (dashed lines) for symmetric $(V_l=25\mathrm{meV})$ and asymmetric $(V_l=32\mathrm{meV})$ quantum dots as function of the magnetic field. Curves for the symmetric case are marked by squares. Inset: Same but for $B=10\mathrm{T}$ as function of $V_l$.

Figure 4

Exchange energy as function of the magnetic field for $V_r=25\mathrm{meV}$ and various values of $V_l$ for which the electrons at high $B$ occupy different dots. Inset: Exchange energy for $V_l=18\mathrm{meV}$ (same as in the main figure) and for $V_l=15$ and 38 meV. For the two latter values the deeper dot is doubly occupied at high $B$.