Flux-dependent Kondo temperature in an Aharonov-Bohm interferometer with an in-line quantum dot

An Aharonov-Bohm interferometer (ABI) carrying a quantum dot on one of its arms is analyzed. It is found that the Kondo temperature of the device may depend strongly on the magnetic flux penetrating the ring. As a result, mesoscopic finite-size effects appear leading to plateaus in the finite-temperature conductance as function of the flux. The possibility to deduce the transmission phase shift of the quantum dot from measurements of the ABI conductance when it is opened (i.e., is connected to more than two leads) is examined, leading to the conclusion that finite-size effects, when significant, may hinder the detection of the Kondo phase shift.

Figure 1

Our model for the ABI with $n_l=n_r=4$, $n_0=2l_0+1=7$. The extremities of the interferometer are denoted by $a$ and $b$. Here $a$ and $b$ correspond, respectively, to points $-4$ and $+4$.

Figure 2

(Color online) Kondo temperatures as function of the AB phase $\alpha =2\pi \Phi ∕{\Phi }_0∊[0,\pi ]$ calculated using either the SBMFT definition, Eq. (9), or the RG definition, Eq. (11), for two different ABI sizes: $L=21$ (the full and long dashed lines) and $L=403$ (the dotted and dashed-dotted lines). The following parameters are used: $j_l=j_r=0.35$, ${ϵ}_d=-0.7$ (giving $T_K^0\sim 0.011$ or ${\xi }_K^0\sim 180$), and $J_L=J_R=0.6$, ${ϵ}_l={ϵ}_r={ϵ}_0=0$.

Figure 3

(Color online) The Kondo temperature as function of the AB phase, $\alpha =2\pi \Phi ∕{\Phi }_0∊[0,\pi ]$, for the small configuration described in Sec. 2B2. The parameters used are $T_B=0.5$, ${ϵ}_d=-0.7$, ${ϵ}_l={ϵ}_r={ϵ}_0=-1$, and $j_l=j_r=0.35$.

Figure 4

(Color online) The conductance as function of the AB phase, $\alpha =2\pi \Phi ∕{\Phi }_0$, for various values of the temperature. The top panel shows the conductance when the dot is in the Kondo regime, and the bottom panel shows it for a noninteracting quantum dot at resonance.

Figure 5

(Color online) The conductance as function of the AB phase $\alpha =2\pi \Phi ∕{\Phi }_0$ for various values of the temperature, for $L=403$ ($n_l=n_r=101$, $n_0=203$). The other parameters are unchanged. The dot is in the Kondo regime.

Figure 6

(Color online) The conductance of the smallest ABI configuration, as function of the AB phase $\alpha =2\pi \Phi ∕{\Phi }_0$ for various values of the temperature.

Figure 7

(Color online) The Kondo temperature of an open ABI as function of the AB phase for $J_X=0.4$ (full line) and $J_X=0$ (dashed line). The other parameters used are $j_l=j_r=0.35$, ${ϵ}_d=-0.7$, $n_l=n_r=3$, $n_0=5$, $J_L=J_R=0.6$.

Figure 8

(Color online) The conductance of the open ABI as function of the AB phase for $T={10}^{-4}$ (upper panel) and $T=3\times {10}^{-3}$ (lower panel) for different values of ${ϵ}_d$: ${ϵ}_d=-0.7$ (full line), ${ϵ}_d=-0.5$ (long-dashed line), ${ϵ}_d=-0.3$ (dotted line), ${ϵ}_d=0$ (short-dashed line), ${ϵ}_d=0.3$ (dashed-dashed-dotted line), ${ϵ}_d=0.5$ (dotted-dotted-dashed line), and ${ϵ}_d=0.7$ (long dashed-dotted line).