Transport Spectroscopy of Kondo Quantum Dots Coupled by RKKY Interaction

We develop the theory of conductance of a quantum dot which carries a spin and is coupled via RKKY interaction to another spin-carrying quantum dot. The found dependence of the differential conductance on the bias and magnetic field at a fixed RKKY interaction strength may allow one to distinguish between the possible ground states of the system. Transitions between the ground states are achieved by tuning the RKKY interaction, and the nature of these transitions can be extracted from the temperature dependence of the linear conductance. The feasibility of the corresponding measurements is evidenced by recent experiments by Craig et al.

Figure 1

The exchange interaction of $S=1/2$ spins of dots $S_1$ and $S_2$ with the 2DEG results in the Kondo effect. The connection by weak contacts $C_1$ and $C_2$ to the bigger open dot $M$ creates the exchange (RKKY) interaction between the two spins. The current $I$ as a function of bias $V$ is measured between source ($s$) and drain ($d$) contacts.

Figure 2

(a) Linear conductance $G_0$ as a function of the RKKY coupling constant $J_{12}$ at $T=0$. The crossover from the triplet state $J_{12}<0$ at $|J_{12}|\gg {\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha }\{T_{\mathrm{K}\alpha }\}$ to a singlet state $J_{12}\gg {\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha }\{T_{\mathrm{K}\alpha }\}$ takes place at $|J_{12}|\lesssim {\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha }\{T_{\mathrm{K}\alpha }\}$ and results in the decrease of $G_0$ from a value close to the unitary limit $G_{\mathrm{U}}$ to a much smaller value controlled by the elastic cotunneling. (b), (c) Differential conductance $G(V)$ at $T=0$ and strong RKKY coupling, $|J_{12}|\gg {\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha }\{T_{\mathrm{K}\alpha }\}$. Solid lines: the second-order in exchange $J_1$ result; dashed lines: schematic representation of the enhancement of $G(V)$ resulting from higher order in $J_1$ calculation.

Figure 3

The contour plot of $f_1(J_{12},V,B)$ is shown in the bias ($V$)—magnetic field ($B$) plane. Function $f_1$ determines the differential conductance $G(V)$ at strong RKKY coupling $|J_{12}|\gg {\mathrm{m}\mathrm{a}\mathrm{x}}_{\alpha }\{T_{\mathrm{K}\alpha }\}$, see Eq. (5).