Kondo effect and Josephson current through a quantum dot between two superconductors

Choi, Myung Suk; Lee, Min Chul; Kang, Kicheon; Belzig, Wolfgang

doi:10.1103/physrevb.70.020502

Cited by 191 publications

(249 citation statements)

References 32 publications

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“…2(d) of Ref. 38, although the broadening of the bound-state peak seen in the figure of CLKB must be artificial. One should note that the first and second excited states are degenerate at φ = π.…”

Section: B the Atomic Limitmentioning

confidence: 94%

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Josephson current through a single Anderson impurity coupled to BCS leads

2008

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We investigate the Josephson current J(φ) through a quantum dot embedded between two superconductors showing a phase difference φ. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U . We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature TK and the superconducting energy gap ∆ or, at appropriate TK /∆, the phase difference φ or the impurity energy is varied. We present accurate zero-as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T = 0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental currentvoltage measurements.

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Section: B the Atomic Limitmentioning

confidence: 94%

“…A non-trivial test for the fRG approximation is to compare critical lines obtained numerically at large ∆/Γ with the exact result Eq. (38). This is done in Fig.…”

Section: B the Atomic Limitmentioning

confidence: 99%

Josephson current through a single Anderson impurity coupled to BCS leads

2008

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“…The GS transition between singlet and doublet is predicted to occur when k B T K ≈ . [25][26][27] When the QD is tuned in an even valley, the GS is always singlet.…”

Section: K B T Kmentioning

confidence: 99%

To Screen or Not to Screen, That is the Question!

Maurand¹,

Schönenberger²

2013

Physics

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We performed tunneling spectroscopy of a carbon nanotube quantum dot (QD) coupled to a metallic reservoir either in the normal or in the superconducting state. We explore how the Kondo resonance, observed when the QD's occupancy is odd and the reservoir is normal, evolves towards Andreev bound states (ABS) in the superconducting state. Within this regime, the ABS spectrum observed is consistent with a quantum phase transition from a singlet to a degenerate magnetic doublet ground state, in quantitative agreement with a single-level Anderson model with superconducting leads.

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“…[3,4] Recently, the interplay of various effects such as Aharanov-Bohm, Fano, Josephson, and Kondo effects have been studied extensively, [5,6,7,8,9,10,11] and interesting phenomena caused by inter-electron interactions have been expected to be seen at low temperatures.…”

Section: Introductionmentioning

confidence: 99%

Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs: Gate-voltage dependence of the conductance

Nisikawa

Oguri

2006

Phys. Rev. B

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The ground-state properties of quartet quantum-dot arrays are studied using the numerical renormalization group (NRG) method with a four-site Hubbard model connected to two noninteracting leads. Specifically, we calculate the conductance and local charge in the dots from the many-body phase shifts, which can be deduced from the fixed-point eigenvalues of NRG. As a function of the on-site energy ǫ d which corresponds to the gate voltage, the conductance shows alternatively wide peak and valley. Simultaneously, the total number of electrons N el in the four dots shows a quantized stair case behavior due to a large Coulomb interaction U . The conductance plateaus of the Unitary limit emerging for odd N el are caused by the Kondo effect. The valleys of the conductance emerge for even N el , and their width becomes substantially large at half-filling. It can be regarded as a kind of the Mott-Hubbard insulating behavior manifesting in a small system. These structures of the plateaus and valleys become weak for large values of the hybridization strength Γ between the chain and leads. We also discuss the parallel conductance for the array connected to four leads.

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Kondo effect and Josephson current through a quantum dot between two superconductors

Cited by 191 publications

References 32 publications

Josephson current through a single Anderson impurity coupled to BCS leads

Josephson current through a single Anderson impurity coupled to BCS leads

To Screen or Not to Screen, That is the Question!

Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs: Gate-voltage dependence of the conductance

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