In a quantum dot hybrid superconducting junction, the behavior of the supercurrent is dominated by Coulomb blockade physics, which determines the magnetic state of the dot. In particular, in a single level quantum dot singly occupied, the sign of the supercurrent can be reversed, giving rise to a π -junction. This 0 − π transition, corresponding to a singlet-doublet transition, is then driven by the gate voltage or by the superconducting phase in the case of strong competition between the superconducting proximity effect and Kondo correlations. In a two-level quantum dot, such as a clean carbon nanotube, 0– π transitions exist as well but, because more cotunneling processes are allowed, are not necessarily associated to a magnetic state transition of the dot. In this proceeding, after a review of 0– π transitions in Josephson junctions, we present measurements of current-phase relation in a clean carbon nanotube quantum dot, in the single and two-level regimes. In the single level regime, close to orbital degeneracy and in a regime of strong competition between local electronic correlations and superconducting proximity effect, we find that the phase diagram of the phase-dependent transition is a universal characteristic of a discontinuous level-crossing quantum transition at zero temperature. In the case where the two levels are involved, the nanotube Josephson current exhibits a continuous 0 − π transition, independent of the superconducting phase, revealing a different physical mechanism of the transition.

0 - π Quantum transition in a carbon nanotube Josephson junction: Universal phase dependence and orbital degeneracy

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of 0 to π transition. These CPR consist of two independent branches corresponding to 0- and π-states of the contact. We have found that depending on the transparency of the SIs tunnel barrier, the decrease in the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference φ or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as 10% under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.

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Protected 0-π states in SIsFS junctions for Josephson memory and logic

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of $0$ to $\pi $ transition. These CPR consist of two independent branches corresponding to $0-$ and $\pi-$ states of the contact. We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference $\varphi$ or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as $10\%$ under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.

/pdf/protected-0-pi-states-in-sisfs-junctions-for-josephson-2u0qj6knmf.pdf

Protected 0-pi states in SIsFS junctions for Josephson memory and logic

We show that a wide class of layered superconductor-ferromagnet ($S/F$) hybrids demonstrates the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase well below the superconducting transition temperature. By decreasing the temperature, one can switch the system from uniform to the FFLO state which is accompanied by the damping of the diamagnetic Meissner response down to zero and also by the sign change in the curvature of the current-velocity dependence. Our estimates show that an additional layer of the normal metal ($N$) covering the ferromagnet substantially softens the conditions required for the predicted FFLO instability, and for existing $S/F/N$ systems, the temperature of the transition into the FFLO phase can reach several kelvins.

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Temperature Controlled Fulde-Ferrell-Larkin-Ovchinnikov Instability in Superconductor-Ferromagnet Hybrids.

This thesis is dedicated to quantum transport through a Kondo impurity, formed in a carbon nanotube quantum dot. We probe the Kondo effect in two situations: in competition with the Josephson effect induced in the nanotube by superconducting contacts and through its high frequency emission. In a first experiment, we have introduced a nanotube in a SQUID in order to measure its supercurrent as a function of the superconducting phase across it. We have measured this quantity in the regime where the Kondo and superconducting correlations are of the same order of magnitude and shown that the ground state of the system, singlet or doublet (corresponding respectively to 0 and π junctions), is then controlled by the superconducting phase. We have also demonstrated that, if a second energy level participates in the transport of Cooper pairs, the 0-π transition is not anymore a first order one as it is the case when only one level is involved. In the second part of the thesis, the carbon nanotube is coupled, at some frequencies determined by a resonator, to a tunnel superconducting junction which is used as an on-chip high-frequency noise detector. This enables the measurement of the emission noise of the quantum dot in the Kondo regime, with reservoirs coupled either symmetrically or not to the dot. Our measurements raise the problem of the spatial asymmetry of the measured noise and seem to show that, the more symmetric is the coupling of the reservoirs to the dot, the more the Kondo resonance is weaken in an out-of-equilibrium situation. Finally, this setup has been used in order to measure the AC Josephson emission of a nanotube contacted with superconducting electrodes, in order to extend our investigation of the competition between the Kondo effect and superconductivity at high frequency. These measurements reveal a decrease of the Josephson emission observed together with a maximum of supercurrent.

Josephson effect and high frequency emission in a carbon nanotube in the Kondo regime

We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $\pi$ (odd) order parameter configurations. The first order $0-\pi$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $\lambda(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev. B 90, 064510 (2014)]. The generalized Ginzburg-Landau functional was proposed to describe SFS trilayer for arbitrary phase difference between the superconducting order parameters in the S layers. The temperature dependence of the SFS Josephson junction critical current demonstrates the strong anharmonicity of the corresponding current--phase relation in the vicinity of the $0-\pi$ transition. In rf SQUID, coexistence of stable and metastable $0$ and $\pi$ states provides integer and half--integer fluxoid configurations.

First order 0-pi phase transitions in superconductor/ferromagnet/superconductor trilayers

The seminal work of Abrikosov on the vortex lattices in type-II superconductors has triggered the creation and rapid development of the whole new field of condensed matter physics, namely, the physics of vortex matter in a large variety of superfluid and superconducting systems. Among these systems and compounds the layered superconductors are known to form a very important class which is associated with a number of fascinating new discoveries in vortex physics. The phenomenon of the vortex attraction in tilted magnetic fields provides one of the examples of such findings which affected theoretical and experimental research in the field for almost two decades. In our paper we review some recent advances in this direction focusing on the intervortex interaction and equilibrium vortex structures in thin films of layered superconductors in magnetic field tilted with respect to the layers. In such a case the magnetic field penetrates superconductor in the form of tilted vortices or a crossing array of Josephson vortices and pancake stacks. We study the interplay between two different long-range potentials: (i) attraction of tilted vortices or deformed stacks; (ii) the Pearl's repulsion. This interplay is responsible for the formation of the minimum in the total interaction energy and resulting decay of vortex chains in clusters. The number of Abrikosov vorti-ces in these clusters (or vortex molecules) depends on field tilting angle and film thickness.

https://hal.archives-ouvertes.fr/hal-01844859/document

A. V. Samokhvalov

Papers

First order 0-pi phase transitions in superconductor/ferromagnet/superconductor trilayers

Vortex molecules in thin films of layered superconductors