Transport through a quantum dot with SU(4) Kondo entanglement

We investigate a mesoscopic setup composed of a small electron droplet (dot) coupled to a larger quantum dot (grain) also subject to Coulomb blockade as well as two macroscopic leads used as source and drain. An exotic Kondo ground state other than the standard SU(2) Fermi liquid unambiguously emerges: an SU(4) Kondo correlated liquid. The transport properties through the small dot are analyzed for this regime, through boundary conformal field theory, and allow a clear distinction with other regimes such as a two-channel spin state or a two-channel orbital state.

Figure 1

(Color online) A small dot in the Kondo regime which acts as an $S=1∕2$ spin impurity is weakly coupled to a large dot (grain) as well as to two leads serving as source and drain.

Figure 2

(Color online) Stability diagram of the dot-grain system. The colored areas indicate where the the novel Kondo fixed points may be found with some fine-tuning of the tunneling amplitudes. Three fixed points are distinguished: 2CK spin (two-channel Kondo spin), 2CK orbital (two-channel Kondo orbital), and SU(4) Kondo are discussed in the sequel. Here, III, V, VI refer to the sections in the text, the mean number of electrons on the dot (grain) is denoted $N_{\mathit{\text{dot}}}$ $\left(N_{\mathit{\text{grain}}}\right)$, and each domain is embodied by a different set $(N_{\mathit{\text{dot}}},N_{\mathit{\text{grain}}})$.

Figure 3

(Color online) Fixed points for a grain at degeneracy. The SU(4) fixed point requires $t\approx t_g$ and is marginally stable. For alarge asymmetry between $t=\sqrt{t_1^2+t_2^2}$ and $t_g$ the small dot will undergo a crossover towards a single-channel Kondo effect either with the reservoir leads or with the grain.