We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interference between the two tunneling processes between the superconductors: the direct tunneling across the insulating barrier and the resonant one through the QD. Moreover, we find that the Josephson critical current changes its sign around the resonance when the Coulomb interaction is sufficiently strong. Our results suggest that $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.
We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interference between the two tunneling processes between the superconductors: the direct tunneling across the insulating barrier and the resonant one through the QD. Moreover, we find that the Josephson critical current changes its sign around the resonance when the Coulomb interaction is sufficiently strong. Our results suggest that 0\ensuremath-\ensuremathπ transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.
We theoretically study the Fano resonance in Josephson current. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). To treat the Coulomb interaction inside the QD, we employ the Hubbard-I approximation, in which the correlation {δ n ↑ δ n ↓ ) can be taken into account beyond the Hartree-Fock approximation. It is found that the dependence of the Josephson critical current on the QD energy level has an asymmetric resonance, which is similar to the Fano resonance in normal metal systems. Moreover, we find that the sign of the critical current can change around the resonance, and such behavior is not seen without the Coulomb interaction. These results indicate that the cooperation of the Fano effect and the Coulomb interaction induces the 0-π transition.
We investigate the influence of the Fano effect on the Josephson current through a quantum dot (QD) coupled to two identical superconductors (SCs). Our attention is focused on the situation where the Kondo spin singlet survives the superconductivity and the finite- U slave-boson mean-field method is adopted to treat the Kondo correlation. With the direct coupling between the two SCs increased, the Josephson current varies in different manners in different regimes. This is consistent with the variation of Josephson coupling, which exhibits characteristics similar to those shown by the conductance through a QD connected to normal leads. But unlike the normal conductance, a negative Josephson coupling region is formed in the dip of the characteristic asymmetric peak–dip structure. Accompanying this 0–π transition, a new kind of intermediate states is found, which are different from those caused by effective ferromagnetic interaction. This 0–π transition and the intermediate states are yielded entirely by the Fano effect.
In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.
We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
The case of a quantum dot connected to two superconducting leads is studied by using the narrow-band limit to describe the superconducting degrees of freedom. The model provides a simple theoretical framework, almost analytical, to analyze the interplay between the Kondo effect, superconductivity, and finite temperature. In the quantum dot Kondo regime, the model is completely characterized by the ratio $\ensuremath{\Delta}/J$, with $\ensuremath{\Delta}$ the superconducting gap and J an effective antiferromagnetic exchange coupling between the dot and the leads. The model allows us to calculate, at any temperature T, the equilibrium Josephson current through the dot in a very straightforward way as a function of $\ensuremath{\Delta}/J$. The behavior of the current allows us to distinguish the four types of hybrid junctions: 0, ${0}^{\ensuremath{'}},{\ensuremath{\pi}}^{\ensuremath{'}}$, and $\ensuremath{\pi}$. The presence of the 0- and ${0}^{\ensuremath{'}}$-junction configurations are intrinsically linked to the Kondo effect in the quantum dot, while the $\ensuremath{\pi}$- and ${\ensuremath{\pi}}^{\ensuremath{'}}$-junction configurations are driven by the superconductivity in the leads. The Josephson critical current has a non-monotonic behavior with temperature, that may be used for the experimental characterization of the fundamental $0\ensuremath{-}\ensuremath{\pi}$ transition. The model allows us to obtain easily a phase diagram $\ensuremath{\Delta}/J$ vs temperature, from where we can obtain an overall picture on the stability of the different types of junctions. From the explicit analytical expressions for the ground-state, low-energy excitations, free energy, and Josephson current, it is easy to understand the physical nature of the main features of the critical current and the phase diagram. The results, obtained with a minimum of numerical effort, are in a good qualitative agreement with more demanding calculational approaches aimed to solve the full model.
Abstract In this study, we investigate the quantum phase transition in a Josephson junction consisting of parallel-connected quantum dots (QDs) with a magnetic flux φ B threading the central region. Employing the surrogate model approach, we discretize the superconducting (SC) electrode into three discrete energy levels, which enables direct diagonalization of the Hamiltonian to determine the system’s ground state. Our calculations demonstrate that when Coulomb interaction is present in only one QD, the system exhibits a phase transition between singlet and doublet states. The magnetic flux exerts a minor influence on the singlet state while substantially affecting the doublet state. When both QDs possess Coulomb interactions, the system undergoes two successive phase transitions as the SC phase difference increases: the ground state evolves from a doublet to a singlet and subsequently to a triplet state at ϕ = π . Enhancement of the magnetic flux suppresses the doublet and triplet phases, ultimately stabilizing the singlet state. Within this regime, increasing the Coulomb interaction strength U does not trigger a singlet-triplet transition; rather, it induces a transition between upper and lower singlet states, resulting in a pronounced peak in the critical current as U increases. Finally, we explore the scenario where the tunneling self-energy Γ between the QDs and SCs exceeds the SC pairing potential Δ. In this case, doublet states prevail, and the system manifests a phase transition exclusively between doublet and triplet states when ϕ B = 0 . Upon application of a magnetic flux, all three states converge, giving rise to a triple point in the ( φ , φ B ) parameter space.