Phase effects on the conductance through parallel double dots

Phase effects on the conductance of a double-dot system in a ring structure threaded by a magnetic flux are studied. The Aharonov-Bohm effect combined with the dot many-body charging effects determine the phases of the currents going through each arm of the ring. The cases for zero magnetic flux or half a quantum of flux are discussed in detail. It is shown that, depending upon the magnetic flux and the state of charge of the dots, controlled by gate potentials, the dephasing of the upper and lower arm current gives rise to a $S=1∕2$ or $S=1$ Kondo regime.

Figure 1

Aharonov-Bohm interferometer with two embedded quantum dots, threaded by a magnetic flux $\Phi$, connected to leads.

Figure 2

Conductance (white, maximum; black, minimum) as a function of the gate potentials at the dots, $V_{\alpha }$ and $V_{\beta }$. $\Phi =0$ (upper panel), $\Phi ={\Phi }_0∕2$ (lower panel); $\Delta E=0$ (continuous line), $\Delta E=0.6$ (dashed line).

Figure 3

Conductance, spin correlation, and charge occupancy for $\Delta E=0.6(V_{\beta }=V_{\alpha }+0.6)$, as a function of $V_{\alpha }$. $\Phi =0$ (left) and $\Phi ={\Phi }_0∕2$ (right). Conductance (a) and (d); spin correlation (b) and (e): $⟨{\vec{S}}_{\alpha }{\vec{S}}_{\beta }⟩$ (continuous line), $⟨{\vec{S}}_{\alpha }{\vec{S}}_c⟩$ (dashed line), and $⟨{\vec{S}}_{\beta }{\vec{S}}_c⟩$ (dotted line); charge occupancy (c) and (f): dot $\alpha$ (continuous line), dot $\beta$ (dashed line). The insets in (a) shows the total dot spin and in (b) the Kondo peak $(\omega =0)$ in the DOS for $V_{\alpha }=-0.6,-0.7,-0.8$.

Figure 4

Transmission through the two ring arms as a function of $V_{\alpha }$, for $\Phi =0$ and $\Delta E=0.6$. (a) phase difference (units of $\pi$); (b) modulus (arbitrary units).