Measuring the Kondo effect in the Aharonov-Bohm interferometer

The conductance $\mathcal{G}$ of an Aharonov-Bohm interferometer (ABI), with a strongly correlated quantum dot on one arm, is expressed in terms of the dot Green function, $G_{dd}$, the magnetic flux $\varphi$ and the noninteracting parameters of the ABI $\left\{J_{\mu \nu }\right\}$. At $T=0$, Fermi liquid theory yields the exact $\varphi$ dependence of $\mathcal{G}$. We show that one can extract $G_{dd}$ from the observed $\mathcal{G}\left(\varphi \right)$, for both closed and open ABI’s. In the latter case, the phase shift $\beta$ deduced from $\mathcal{G}\approx A+B\cos (\varphi +\beta )$ depends strongly on the $\left\{J_{\mu \nu }\right\}$’s, and usually $\beta \ne \pi ∕2$. The $\left\{J_{\mu \nu }\right\}$’s may also reduce the Kondo temperature.

Figure 1

The model for the ABI, with $n_l=n_r=3$, $n_0=5$.

Figure 2

(Color online) Conductance (in units of $2e^2∕h$) through the closed ABI versus the normalized flux $\varphi$ and the energy of the state on the dot ${ϵ}_d$ (the gate voltage), without (top) and with interactions (bottom). $n_l=n_r=2$, $n_0=3$, $J_L=J_R=J_D=1$, $j_l=j_r=0.2$, $i_l=i_r=0.4$, ${ϵ}_l={ϵ}_r={ϵ}_0=-0.3$, ${ϵ}_L={ϵ}_R=0$. All energies are in units of $J$.

Figure 3

Top: Conductance through the open ABI versus $\varphi$, at ${ϵ}_d=(-1.5,-1,-0.5,0,0.5,1,1.5)J$, with infinite interactions. Graphs are shifted up with increasing ${ϵ}_d$. Parameters are the same as in Fig. 2, but with $J_X=0.5$. Bottom: The “measured” phase shift $\beta$ (in units of $\pi$) versus ${ϵ}_d$.