Numerical Renormalization Group Study of Magnetic Impurities in Superconductors

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

doi:10.1143/jpsj.61.3239

Cited by 168 publications

(220 citation statements)

References 16 publications

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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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“…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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“…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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“…Most of these studies effectively neglect the presence of superconducting (sc) fluctuations in the host, i.e., they use the local fermionic density of states (DOS) as the only input quantity characterizing the environment of the Kondo impurity. For s-wave superconductors it has been shown [1] that this approximation is not justified: here the properties of a Kondo impurity are different from the ones of an impurity embedded in a non-superconducting system with the same DOS. More precisely, the superconducting bath turns out to be equivalent to a non-superconducting bath with additional particle-hole (p-h) asymmetry [1].…”

mentioning

confidence: 99%

“…For s-wave superconductors it has been shown [1] that this approximation is not justified: here the properties of a Kondo impurity are different from the ones of an impurity embedded in a non-superconducting system with the same DOS. More precisely, the superconducting bath turns out to be equivalent to a non-superconducting bath with additional particle-hole (p-h) asymmetry [1]. As a result, for a p-h symmetric conduction band a screened singlet state is realized at large Kondo coupling, in contrast to the non-sc case with a hard gap in the local DOS [11].…”

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confidence: 99%

Kondo screening in unconventional superconductors: The role of anomalous propagators

Fritz

Vojta

2005

Phys. Rev. B

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The Kondo effect in superconductors is frequently investigated using the local quasiparticle density of states as sole bath characteristics, i.e., the presence of anomalous propagators is ignored. Here we point out that this treatment is exact for a number of situations, including point-like impurities in dwave superconductors. We comment on recent investigations [M. M. Koga, J. Phys. Soc. Jpn. 70, 2860 (2001) and Phys. Rev. B 65, 024508 (2002)] which reached different conclusions: while their numerical results are likely correct, their interpretation in terms of two-channel Kondo physics and an "orbital effect of Cooper pairs" is incorrect.PACS numbers: 75.20.Hr, The physics of quantum impurity moments in superconductors, associated with the Kondo effect, has been subject of numerous investigations in recent years. Diverse theoretical techniques have been employed to study Kondo or Anderson models in a superconducting environment [1][2][3][4][5][6][7][8][9]. Most of these studies effectively neglect the presence of superconducting (sc) fluctuations in the host, i.e., they use the local fermionic density of states (DOS) as the only input quantity characterizing the environment of the Kondo impurity. For s-wave superconductors it has been shown [1] that this approximation is not justified: here the properties of a Kondo impurity are different from the ones of an impurity embedded in a non-superconducting system with the same DOS. More precisely, the superconducting bath turns out to be equivalent to a non-superconducting bath with additional particle-hole (p-h) asymmetry [1]. As a result, for a p-h symmetric conduction band a screened singlet state is realized at large Kondo coupling, in contrast to the non-sc case with a hard gap in the local DOS [11]. This difference can be understood as caused by the anomalous bath propagators.In this Brief Report, we address the role of anomalous propagators in unconventional superconductors. We argue below that neglecting sc propagators is exact in many, potentially experimentally relevant, cases, e.g., for point-like impurities in d-wave and unitary p-wave superconductors. In these situations, the dynamics of the impurity degrees of freedom can be calculated using the normal bath propagators only. We also comment on recent papers by Matsumoto and Koga who argued in favor of a non-trivial "orbital effect of Cooper pairs" for pointlike impurities in both p + ip and d + id superconductors [7,8]. While we believe that their numerical results are correct, we point out that such an orbital effect does not exist: in their situation the impurity properties are exclusively determined by the local DOS.We start from the action of an Anderson impurity in a general interacting host.where β = 1/T is the inverse temperature, c are the conduction electrons with dispersion ǫ k on a regular lattice with N sites, S int are the interactions within the conduction band, and S loc describes the f electron impurity orbital with on-site energy and repulsion. The sum {i} runs over a set of lattic...

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Numerical Renormalization Group Study of Magnetic Impurities in Superconductors

Cited by 168 publications

References 16 publications

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

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

Josephson current through a single Anderson impurity coupled to BCS leads

Kondo screening in unconventional superconductors: The role of anomalous propagators

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