Quantum Dot in the Kondo Regime Coupled to Superconductors

The Kondo effect and superconductivity are both prime examples of many-body phenomena. Here we report transport measurements on a carbon nanotube quantum dot coupled to superconducting leads that show a delicate interplay between both effects. We demonstrate that the superconductivity of the leads does not destroy the Kondo correlations on the quantum dot when the Kondo temperature, which varies for different single-electron states, exceeds the superconducting gap energy.

Figure 1

(a) Grey scale representation of the differential conductance as a function of source drain ($V_{\mathrm{s}\mathrm{d}}$) and gate voltage ($V_g$) at $T=50\mathrm{m}\mathrm{K}$ and $B=26\mathrm{m}\mathrm{T}$ for a MWNT device in the Kondo regime (darker areas $=$ more conductive). The dashed white lines outline the Coulomb diamonds. The black curve shows the $dI/d{V}_{\mathrm{s}\mathrm{d}}$ versus $V_{\mathrm{s}\mathrm{d}}$ trace at the position of the arrow. The regions with even and odd number of electrons are labeled $E$ and $O$, respectively. (b) Linear-response conductance $G$ as a function of $V_g$. The Kondo ridges are labeled $A$, $B$, and $C$. (c),(d) Temperature dependence of ridge $A$ between 50 mK (thicker line) and 700 mK (dashed line). The data can be fitted using the empirical function given in the text yielding a Kondo temperature for ridge $A$ of $\sim 0.75\mathrm{K}$. (e) When a magnetic field is applied (0.1–2 T), the ridges split into components at $V_{\mathrm{s}\mathrm{d}}=\pm g{\mu }_{B}B/e$.

Figure 2

(a) Grey scale representation of the differential conductance as a function of $V_{\mathrm{s}\mathrm{d}}$ and $V_g$ at $T=50\mathrm{m}\mathrm{K}$ and $B=0\mathrm{m}\mathrm{T}$ for the same gate region as in Fig. 1. The dotted white lines indicate the shift of the Andreev peaks. (b) Linear-response conductance $G$ as a function of $V_g$. (c) Schematics (simplified) of a quantum dot between superconductors showing two Andreev reflections. (d)–(f) $dI/dV$ versus $V_{\mathrm{s}\mathrm{d}}$ for the $V_g$ positions indicted by the arrows in panel (b).

Figure 3

(a) $dI/dV$ grey scale plot for three different Kondo ridges at $T=50\mathrm{m}\mathrm{K}$ and $B=26\mathrm{m}\mathrm{T}$. The $dI/d{V}_{\mathrm{s}\mathrm{d}}$ versus $V_{\mathrm{s}\mathrm{d}}$ traces are measured in the middle of the ridges. (b) The same plot for the superconducting state. An intricate pattern develops showing multiple Andreev peaks, the position and magnitude of which depend on the level position. (c) Linear-response conductance in the normal (solid lines) and superconducting (dashed lines) state. The rightmost plot shows that even if the conductance modulation in the normal state is weak and $G\sim 2e^2/h$ both for $S=0$ and $S=1/2$, the difference can be dramatic when the leads are superconducting.

Figure 4

The data points give the ratio $G_S/G_N$ of the conductances in the middle of 12 different Kondo ridges in the superconducting ($G_S$) and normal ($G_N$) state versus $T_K/\Delta$ measured at $T=50\mathrm{m}\mathrm{K}$. The gap energy $\Delta$ is 0.1 meV, corresponding to 1.16 K. The numbers indicate $G_N$ in units of $e^2/h$ for each data point [23]. The dashed line is a guide to the eye.