Numerical Renormalization Group Study of Magnetic Impurities in Superconductors. II. Dynamical Excitation Spectra and Spatial Variation of the Order Parameter

Sakai, Osamu; Shimizu, Yukihiro; Shibata, Hiroyuki; Satori, Koji

doi:10.1143/jpsj.62.3181

Cited by 100 publications

(123 citation statements)

References 14 publications

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“…Therefore, the eigenvalue Q of the operator Q ps can be used as a quantum number to classify the Hilbert space in addition to the total spin S associated with the rotational symmetry of the real spin. 53,54 APPENDIX B: CURRENT FORMULA In this section we derive an exact formula relating the Josephson current to the self-energy. To this end, we define a current operator at lead s = L, R as usual,…”

Section: Appendix A: Nrg Approachmentioning

confidence: 99%

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: Appendix A: Nrg Approachmentioning

confidence: 99%

Josephson current through a single Anderson impurity coupled to BCS leads

2008

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“…[7][8][9][10] Furthermore, it has also been reconsidered for novel systems such as quantum dots. 11,12 One of the new features in the quantum dot coupled to two SC leads is that the ground-state properties of the system can be controlled by the phase difference of the two SC gaps φ.…”

Section: Introductionmentioning

confidence: 99%

Quantum Phase Transition in a Minimal Model for the Kondo Effect in a Josephson Junction

2004

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We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps ∆α = |∆α| e iθα , where α = L, R for the lead at left and right. We show that, when one of the SC gaps is much larger than the others |∆L| ≫ |∆R|, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of ∆R and the Anderson impurity with an extra onsite SC gap of ∆ d ≡ ΓL e iθ L . Here θL and ΓL are defined with respect to the starting model, and ΓL is the level width due to the coupling with the left lead. Based on this simplified model, we study the ground-state properties for the asymmetric gap, |∆L| ≫ |∆R|, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps φ ≡ θR − θL, which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.

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“…For simplicity, we have used the same values for both the superconducting cutoff energy and the band width k F , since it is assured that this does not alter the results. 9 The fermion represented by the operator f 00σ corresponds to a fermion localized at the impurity. The first subscript 0 of f 00σ represents the 0-th shell of the NRG Hamiltonian which will be derived later (see Appendix).…”

Section: A Model Hamiltonianmentioning

confidence: 99%

“…In our formulation we follow the procedure by Sakai et al 9 and derive a NRG Hamiltonian. There is another way to derive the Hamiltonian, 8 which we describe in Appendix.…”

Section: B Transformation Of the Hamiltonianmentioning

confidence: 99%

“…[6][7][8][9][10] The numerical renormalization group (NRG) study by Satori et al 8 showed that the bound state energy is scaled by T K /∆ and the interchange of singlet and doublet ground states occurs smoothly. Even if an energy gap exists in the density of quasiparticle states, a local spin couples with the quasiparticles antiferromagnetically to form a spin singlet (Kondo singlet) for T K /∆ > 0.3.…”

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Orbital effect of Cooper pairs on the Kondo effect in unconventional superconductors

Matsumoto

Koga

2001

Phys. Rev. B

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A new type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using the Wilson's numerical renormalization group method. In this case, an angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a px + ipy-wave state which is a full gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong coupling region (TK/∆ → ∞), while the ground state is always a spin doublet over all the TK/∆ region. Here TK and ∆ are the Kondo temperature and the superconducting energy gap, respectively. This is different from the s-wave pairing case where the Kondo singlet is realized for large TK/∆ values. The strong coupling analysis shows that the px + ipy-wave Cooper pair is connected to the Kondo singlet via the orbital dynamics of the paired electrons, generating the spin of the ground state. This type of Kondo effect reflects the symmetry of the conduction electron system.

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Numerical Renormalization Group Study of Magnetic Impurities in Superconductors. II. Dynamical Excitation Spectra and Spatial Variation of the Order Parameter

Cited by 100 publications

References 14 publications

Josephson current through a single Anderson impurity coupled to BCS leads

Josephson current through a single Anderson impurity coupled to BCS leads

Quantum Phase Transition in a Minimal Model for the Kondo Effect in a Josephson Junction

Orbital effect of Cooper pairs on the Kondo effect in unconventional superconductors

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