Probing spin and orbital Kondo effects with a mesoscopic interferometer

We investigate theoretically the transport properties of a closed Aharonov-Bohm interferometer containing two quantum dots in the strong coupling regime. We find two distinct physical scenarios depending on the strength of the interdot Coulomb interaction. When the interdot Coulomb interaction is negligible, only spin fluctuations are important and each dot develops a Kondo resonance at the Fermi level independently of the applied magnetic flux. The transport is characterized by the interference of these two independent Kondo resonances. On the contrary, for large interdot interaction, only one electron can be accommodated onto the double-dot system. In this situation, not only the spin can fluctuate but also the orbital degree of freedom (the pseudospin). As a result, we find different ground states depending on the value of the applied flux. When $\varphi =\pi \left(\mathrm{mod}2\pi \right)$ ($\varphi =2\pi \mathrm{\Phi }∕{\mathrm{\Phi }}_0$, where $\mathrm{\Phi }$ is applied flux and ${\mathrm{\Phi }}_0=h∕e$ the flux quantum) the electronic transport can take place via simultaneous correlations in the spin and pseudospin sectors, leading to the highly symmetric SU(4) Kondo state. Nevertheless, we find situations with $\varphi >0\left(\mathrm{mod}2\pi \right)$ where the pseudospin quantum number is not conserved during tunneling events, giving rise to the common SU(2) Kondo state with an enhanced Kondo temperature. We investigate the crossover between both ground states and discuss possible experimental signatures of this physics as a function of the applied magnetic flux.

Figure 1

Sketch of the Aharonov-Bohm interferometer containing two quantum dots attached to two leads. The arrowed straight line indicates the tunnel coupling and the dashed line represents the interdot Coulomb interaction.

Figure 2

SBMFT results: Left panel $(U_{12}\to 0)$: (a) Linear conductance $\left({\mathcal{G}}_0\right)$ versus flux $\varphi$ for different level positions. When the Kondo state is formed (for ${\epsilon }_d=-3.5$) the ${\mathcal{G}}_0$ are delta-like peaks of height 1 centered at even multiples of $\varphi ∕\pi$. (c) Curves for $\mathcal{G}$ versus voltage bias for ${\epsilon }_d=-3.5$. Here, we change the flux from 0 (full line) to $\pi$ (dot-dot-dashed line). Right panel $(U_{12}\to \mathrm{\infty })$: (b) linear and (d) differential conductance. Energies are measured in units of $\mathrm{\Gamma }=\pi {\rho }_0{\mid V\mid }^2=D∕60$.

Figure 3

NRG results: Top panel: Transmission probability versus flux for (a) ${\epsilon }_d=-7\mathrm{\Gamma }$, $U_1=U_2=5D$, $U_{12}=0$, and (b) ${\epsilon }_d=-14\mathrm{\Gamma }$, $U_1=U_2=5D$, and $U_{12}=5D$. We set $\mathrm{\Gamma }=D∕60$. [Notice that we do not recover the unitary limit of $\mathcal{T}$ for $\varphi \approx 0\left(\mathrm{mod}2\pi \right)$ because of the systematic errors introduced in the NRG procedure]. Bottom panel $\left(U_{12}=5D\right)$: (c) Spin susceptibility (in an arbitrary unit) in the limit of strong interdot interaction. (d) The peak position of the susceptibility as a function of the flux $\varphi$.