Figure 1

(Color online) (a) The persistent current as a function of magnetic field at different $d$ in two interacting QRs containing each three electrons without interring tunneling. (b) The phase diagram in the $B\text{−}d$ plane. The dashed horizontal lines indicate the transitions in a single ring. Each phase is indicated by two quantum numbers $\left(S_z,M_z\right)$. The inset shows the energy difference $\Delta E^{\text{inter}}$ of the inter-ring Coulomb energy between the different configurations at a fixed magnetic field. (c) Variation in the persistent current in the rings as a function of $d$ at $B=0.7$, 0.85, and 1.2 T. The horizontal lines are the current for the single ring case.Reuse & Permissions

Figure 2

(a) The total persistent, (b) the paramagnetic, and (c) the diamagnetic currents as a function of magnetic field in the CQRs of $d=0.1r_0$ and with $N=3$ electrons. (d) The same as (a) but now for $N=6$. The different phases are indicated by $\left(S_z,M_z,I_z\right)$.Reuse & Permissions

Figure 3

The phase diagrams of the ground-state configurations of the CQRs of $N=6$ electrons. The three quantum numbers $\left(S_z,M_z,I_z\right)$ indicate the ground-state configuration.Reuse & Permissions

Figure 4

(Color online) (a) The persistent, (b) the paramagnetic, and (c) the diamagnetic currents in the CQRs with $d=0.23r_0$ and $N=3$ electrons. The dotted (red) and dashed (blue) curves are currents carried by the bonding and antibonding states, respectively. The persistent current in the CQRs of $N=6$ electrons at (d) $d=0.23r_0$ and (e) $0.40r_0$. The thin dash-dotted curves are the current in the corresponding coupled rings without tunneling. Each GS phase is indicated by $\left(S_z,M_z,I_z\right)$.Reuse & Permissions