Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase

The magnetic state of a quantum dot attached to superconducting leads is experimentally shown to be controlled by the superconducting phase difference across the dot. This is done by probing the relation between the Josephson current and the superconducting phase difference of a carbon nanotube junction whose Kondo energy and superconducting gap are of comparable size. It exhibits distinctively anharmonic behavior, revealing a phase-mediated singlet-to-doublet transition. We obtain an excellent quantitative agreement with numerically exact quantum Monte Carlo calculations. This provides strong support that we indeed observed the finite-temperature signatures of the phase-controlled zero temperature level crossing transition originating from strong local electronic correlations.

Figure 1

(a) Scanning electron microscopy image of the measured asymmetric SQUID (see text and [31]). (b) Differential conductance ($\frac{dI}{d{V}_{sd}}$) in the normal state of the CNT junction versus gate voltage $V_g$ and bias voltage $V_{sd}$ for a large range of $V_g$. Panels (c) and (d) focus on two Kondo zones called respectively A and B. A 1 T magnetic field is applied to destroy superconductivity in the contacts. The number of electrons in the last occupied energy levels is indicated in white. In light blue, $\frac{dI}{d{V}_{sd}}\left(V_{sd}\right)$ at zero bias is plotted (axis on the right). In the normal state, the reference JJ contribution is a constant which was subtracted to obtain the plots. The white symbols in (c) correspond to the theoretical fit of the conductance (see text).

Figure 2

(a) Modulation of the switching current of the SQUID, proportional to the CPR of the CNT junction, versus the magnetic field for various gate voltages in zone A. (b) Modulation of the switching currents near the transition for several gate voltages. (c) CPR extracted from the previous data and rescaled by 1.33 (see the text) near the transition (green continuous line). The theoretical predictions resulting from QMC calculations are shown as black lines. The dashed lines are guides to the eyes and represent the contributions of the singlet (0 junction, in blue) and the doublet state ($\pi$ junction, in red).

Figure 3

(a) Modulation of the switching current of the SQUID for zone B, which exhibits a partial transition from 0 to $\pi$ junction. (b) CPR extracted from the previous data near the transition (green continuous line). The dashed lines are guides to the eyes and represent the contributions of the singlet (0 junction in blue) and the doublet state ($\pi$ junction in red).

Figure 4

(a) Calculated $T_K$ (black line) is compared to $\mathrm{\Delta }$ (dotted line) as a function of the level energy $\epsilon$ ($\epsilon =\alpha \delta V_g$ with $\delta V_g$ the gate value measured from half filling and $\alpha =39\mathrm{meV}/\mathrm{V}$). In green dots, the critical phase ${\phi }_C$ is plotted, defined as the phase, different from 0 and $\pi$, for which the CPR equals zero [see text and inset of (c)]. The 0-$\pi$ transition occurring when ${\phi }_C$ switches from 1 to 0, the system is indeed in the regime $k_B{T}_K\approx \mathrm{\Delta }$. (b) Fourier analysis of the CPRs of zone A near the transition for different level energies $\epsilon$. The circles correspond to the experimental CPRs whereas the continuous lines correspond to the QMC calculation (red, blue, and black: harmonics 1, 2, and 3). (c) Measured ${\phi }_C$ (red circles) versus $\epsilon$. ${\phi }_C$ extracted from the QMC calculation and shifted is also shown (blue squares). The black line shows the result of a two-parameter fit of the analytical curve obtained in the atomic limit (see text).