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How to control the magnetic state of a quantum dot with the superconducting phase ?

A mesoscopic conductor connected to superconducting electrodes can sustain a supercurrent, which is a periodic function of the phase difference between the two superconductors. The amplitude and the phase-dependence of the supercurrent provide information on the nature and symmetry of the quantum states confined in the nanostructure. In the case of a quantum dot it becomes possible to probe an intriguing situation, in which the superconducting proximity effect competes with another type of electronic correlation : the Kondo effect.

By finely tuning the coupling between the quantum dot and the electrodes, the spin of the dot’s highest occupied energy levels is screened by the electrodes’ conduction electrons. This constitutes a correlated singlet state between the dot’s spin and the electrodes. Such a correlated state forms below a characteristic temperature, the Kondo temperature TK, and leads to a resonance in the conduction properties of the quantum dot. For a quantum dot connected to superconducting contacts, this Kondo effects persists even when the superconducting gap Δ is smaller than kBTK. In that case the two effects cooperate the supercurrent is largest (“junction 0”). In the opposite limit (Δ > kBTK) the magnetic moment of the quantum dot is not screened : this leads to a reduction and a sign change of the supercurrent, a “π junction”.

Figure  : Left  : Image taken with an electron microscope of the measured sample (CNT : carbon nanotube, JJ : Josephson junction). Right  : Measured current phase relation (green line) close to the 0-π transition, compared to the theoretical prediction (black line).The dashed line represents the singlet (0 junction, in blue) and doublet contributions (π junction, in red).

Experimentalists of the Laboratoire de Physique des Solides have demonstrated for the first time the control by the superconducting phase of the magnetic state of a quantum dot. It happens in the regime of strongest competition between the Kondo and the superconducting proximity effect (Δ ∼ kBTK). This has spectacular consequences on the relation between the supercurrent and the superconducting phase : the current phase relation. Indeed the junction behaves both as a 0 junction and a π junction (see the Figure) ! To create this experiment, a carbon nanotube, which acts as a quantum dot, is inserted in a SQUID (Superconducting Quantum Interference Device) and measured at very low temperature. The current-phase relation is extracted from the supercurrent of the SQUID which is modulated by the phase difference controlled by a magnetic field. A successful comparison with theoretical prediction was carried out thanks to a collaboration with theorists from Aachen and Toulouse. This experiment demonstrates the control of the magnetic state of a quantum dot by the superconducting phase and paves the way to current phase relation measurements in strongly correlated mesoscopic systems.

Reference :
Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase
R. Delagrange, D. J. Luitz, R. Weil, A. Kasumov, V. Meden, H. Bouchiat, R. Deblock.
Phys. Rev. B 91, 241401(R) (2015).

Contacts :
Richard Deblock, Hélène Bouchiat