Minimal realization of the orbital Kondo effect in a quantum dot with two leads

We demonstrate theoretically how the Kondo effect may be observed in the transport of spinless electrons through a quantum dot. The role of conduction-electron spin is played by a lead index. The Kondo effect takes place if there are two close levels in the dot populated by a single electron. For temperatures exceeding the Kondo temperature $T⪢T_K$, the conductance is maximal if the levels are exactly degenerate. However, at zero temperature, the conductance is zero at the SU(2) symmetric point but reaches the unitary limit $G=e^2∕h$ for some finite value of the level splitting $\Delta \epsilon \sim T_K$. Introducing the spin $1∕2$ for electrons and having two degenerate orbital levels in the dot allows to observe the SU(4)-Kondo effect in a single dot coupled to two leads.

Figure 1

The conductance of a quantum dot (1,9) as a function of $B∕T_K$ for $\sin 2\varphi =1$. Lower short-dashed line: high temperature conductance, $T=15T_K$, but with only non-spin-flip processes taken into account, Eq. (12). The cut off in Eq. (8) is chosen in a form $D=\sqrt{B^2+T^2}$. Long-dashed line: the same $T=15T_K$, but with the spin-flip current added, Eq. (14). The conductance is doubled at $B⪡T$. Lower solid line [SU(2)]: exact Bethe ansatz at $T=0$ [Eq. (17)]. The conductance vanishes at $B=0$ and reaches the unitary limit, $G=e^2∕h$, at $B=2.43T_K$. Upper solid line: schematic conductance (divided by 2) in the case of two orbital levels with spin [Eq. (21)]. The conductance vanishes at the SU(4) symmetric point, $B=0$, and reaches the unitary limit, $G=2e^2∕h$, at $\mid B\mid ⪢T_K$. The conductance at high temperatures in the case with spin is qualitatively similar to the conductance for spinless electrons, having a pronounced maximum at $B=0$ [Eq. (19)].

Figure 2

Contour plot of the conductance on the $B_z,B_x$ plane at $T=15T_K$, Eq. (14). The conductance is maximal at $\vec{B}=0$, but the peak has zero width in the $B_x$ direction. At zero temperature a valley with conductance $G(B_z=0)=0$ develops along the $B_x$ axis, separating two peaks with $G=e^2∕h$.