A Simple Perturbation Theory of a Quantum Dot Coupled to Superconducting Leads

Matsumoto, Daichi

doi:10.1143/jpsj.70.492

Cited by 9 publications

(19 citation statements)

References 21 publications

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“…We mention in passing that the critical current never exceeded I 0 , in contrast to the prediction in Ref. [15].…”

contrasting

confidence: 79%

“…This paper provides numerically exact results for a magnetic Josephson junction from Monte Carlo (MC) simulations, using a Hirsch-Fye algorithm [19,20,21] adapted to this problem. We find that previous approximate theories for this problem, relying on the non-crossing approximation (NCA) for U → ∞ [10,11,13], mean-field approaches [9,17], perturbative schemes [14,15,16,17], or the numerical renormalization group (NRG) [12,18], lead to incomplete and sometimes even qualitatively inaccurate predictions. Although the existence of the abovementioned phases follows already from mean-field theory [9], their respective stability and the actual phase boundaries have not been reliably established.…”

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confidence: 99%

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Josephson Current through a Nanoscale Magnetic Quantum Dot

2004

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We present theoretical results for the equilibrium Josephson current through an Anderson dot tuned into the magnetic regime, using Hirsch-Fye Monte Carlo simulations covering the complete crossover from Kondo-dominated physics to π junction behavior in a numerically exact way. Within the 'magnetic' regime, U/Γ ≫ 1 and ǫ0/Γ ≤ 1, the Josephson current is found to depend only on ∆/TK , where ∆ is the BCS gap and TK the Kondo temperature. The junction behavior can be classified into four different quantum phases. We describe these behaviors, specify the associated three transition points, and identify a local minimum in the critical current of the junction as a function of ∆/TK . PACS numbers: 74.50.+r, 72.15.Qm, 75.20.Hr Recent advances in nanoscale manipulation and fabrication call for a deeper understanding of the effect of electronic correlations. Due to the complexity of its theoretical treatment, the interplay between superconductivity and magnetism belongs to the least understood phenomena in that respect. Here we study the Josephson current I(φ) through a correlated nanoscale quantum dot contacted by s-wave BCS superconductors. At low enough temperatures, such a dot is generally described by the Anderson impurity model indicated in Fig. 1. We consider the regime U/Γ ≫ 1 and ǫ 0 /Γ ≪ −1, where the dot effectively has single occupancy and thus represents a spin-1/2 degree of freedom. Then a complicated interplay between this magnetic impurity and the superconductivity in the leads sets in. Some aspects of this physics were recently observed in Andreev conductance measurements for a short multi-wall nanotube [1,2]. A similar setup should also allow to probe the Josephson current in the near future, where the ratio ∆/T K is widely tunable via a backgate voltage.In this paper, we provide a detailed analysis and classification of all possible phases expected in such an experiment. We find that only one 'master' parameter ∆/T K governs this problem, whereis the Kondo temperature for normal leads [3]. For ∆/T K ≪ 1, the Kondo effect survives and is only weakly affected by superconductivity, while for ∆/T K ≫ 1, perturbation theory in Γ yields an inverted Josephson relation I(φ) = −I c sin φ [4,5,6,7], where φ = π represents a minimum of the junction free energy F (φ). Such a π junction behavior was recently reported in Nb-Cu x Ni 1−x -Nb systems [8], is related to subgap (Andreev) bound states [9,10], and implies broken time-reversal symmetry. In both limits, analytical expressions [6] are reproduced by our method below. For a magnetic impurity, the Josephson relation is generally replaced by a more complicated dependence on φ. A classification into four types of junctions, labeled as 0, 0 ′ , π ′ and π, follows from the respective stability of the φ = 0 and φ = π configurations [9].For a 0 (π) junction, only φ = 0 (φ = π) is a minimum of F (φ). For the two other cases, both φ = 0, π are local minima, and depending on whether φ = 0 (φ = π) is the global minimum, one has a 0 ′ (π ′ ) junction. Using I(φ) = (2e/ )d...

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“…We mention in passing that the critical current never exceeded I 0 , in contrast to the prediction in Ref. [15].…”

contrasting

confidence: 79%

mentioning

confidence: 99%

Josephson Current through a Nanoscale Magnetic Quantum Dot

2004

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“…The diagonal mean field self-energy is frequencyindependent. 60 This leads to a vanishing Kondo temperature T K , i.e., it is insensitive to interaction-see next section.…”

Section: Going Beyond Mean Fieldmentioning

confidence: 98%

“…Ishizaka calculated the Josephson current numerically within the non-crossing approximation; it was reported that as a function of the Coulomb repulsion the supercurrent is suppressed until at some critical value a sudden sign change occurs 56,57 . Within the numerical renormalization technique, it was reported that a π-junction is the preferred state in junction when the impurity is singly occupied and the onsite Coulomb interaction is large [58][59][60] . A generalization of the non-crossing approximation found a modification in this 0 to π junction transition at the presence of bound states 61 .…”

Section: Introductionmentioning

confidence: 99%

Noise and microresonance of critical current in Josephson junction induced by Kondo trap states

Ansari

Wilhelm

2011

Phys. Rev. B

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We analyze the impact of trap states in the oxide layer of a superconducting tunnel junctions, on the fluctuation of the Josephson critical-current, thus on coherence in superconducting qubits. Two mechanisms are usually considered: the current blockage due to repulsion at the occupied trap states, and the noise from electrons hopping across a trap. We extend previous studies of noninteracting traps to the case where the traps have onsite electron repulsion inside one ballistic channel. The repulsion not only allows the appropriate temperature dependence of 1/f -noise, but also the control of the coupling between the computational qubit and the spurious two-level systems inside the oxide dielectric. We use second-order perturbation theory, which allows to obtain analytical formulas for the interacting bound states and spectral weights, limited to small and intermediate repulsions.Remarkably, it still reproduces the main features of the model as identified from the numerical renormalization group. We present analytical formulations for the subgap bound-state energies, the singlet-doublet phase boundary, and the spectral weights. We show that interactions can reverse the supercurrent across the trap. We finally work out the spectrum of junction resonators for qubits in the presence of onsite repulsive electrons and analyze its dependence on microscopic parameters that may be controlled by fabrication.

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“…Then, the Cooper pair feels the localized magnetic moment in the QD. Under this situation, when the Coulomb interaction is strong inside the QD, so-called 0-π transition occurs 24,25,26,27,28 . It means that the dependence of the Josephson current on the phase difference θ changes from I = |I c | sin θ to I = |I c | sin(θ + π) = −|I c | sin θ, i.e., the critical current becomes negative.…”

Section: Introductionmentioning

confidence: 99%

Fano effect in a Josephson junction with a quantum dot

2008

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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-π transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.

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A Simple Perturbation Theory of a Quantum Dot Coupled to Superconducting Leads

Cited by 9 publications

References 21 publications

Josephson Current through a Nanoscale Magnetic Quantum Dot

Josephson Current through a Nanoscale Magnetic Quantum Dot

Noise and microresonance of critical current in Josephson junction induced by Kondo trap states

Fano effect in a Josephson junction with a quantum dot

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