Kondo impurity between superconducting and metallic reservoir: the flow equation approach

Zapalska, M.; Domański, T.

doi:10.48550/arxiv.1402.1291

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…We may contrast these results with the work based on the continuous unitary transformation (CUT) [44], which is essentially a continuous version of the Schrieffer-Wolff transformation. That work was done in the ∆ → ∞ limit, resulting in the effective Kondo exchange coupling constant J = −4U |V N | 2 /(U 2 + 4∆ 2 d ), where ∆ d is the proximity-induced on-dot pairing ∆ d = Γ SC /2.…”

Section: Discussionmentioning

confidence: 99%

“…This state of affairs motivates a detailed study of the minimal Anderson model incorporating both superconducting lead and normal-state tunneling probe, and fully taking into account quantum fluctuations for an arbitrary ratio of the gap to the Kondo temperature. While many theoretical papers have already studied transport in normal-quantum dot-superconductor system [40][41][42][43][44], the precise role that the coupling Γ N to the normal lead has on the phase diagram (beyond trivial broadening effects) remains largely unknown. The presence of the tunneling probe not only trivially broadens the sub-gap bound states into resonances of finite width, but also leads to further Kondo screening that generates an additional spectral peak pinned to zero frequency.…”

Section: Motivation and Introductionmentioning

confidence: 99%

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Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

et al. 2015

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Hybrid semiconductor-superconductor systems are interesting melting pots where various fundamental effects in condensed matter physics coexist. For example, when a quantum dot is coupled to a superconducting electrode two very distinct phenomena, superconductivity and the Kondo effect, compete. As a result of this competition, the system undergoes a quantum phase transition when the superconducting gap ∆ is of the order of the Kondo temperature TK . The underlying physics behind such transition ultimately relies on the physics of the Anderson model where the standard metallic host is replaced by a superconducting one, namely the physics of a (quantum) magnetic impurity in a superconductor. A characteristic feature of this hybrid system is the emergence of subgap bound states, the so-called Yu-Shiba-Rusinov (YSR) states, which cross zero energy across the quantum phase transition, signaling a switching of the fermion parity and spin (doublet or singlet) of the ground state. Interestingly, similar hybrid devices based on semiconducting nanowires with spin-orbit coupling may host exotic zero-energy bound states with Majorana character. Both, parity crossings and Majorana bound states (MBS)s, are experimentally marked by zero bias anomalies in transport, which are detected by coupling the hybrid device with an extra normal contact. We here demonstrate theoretically that this extra contact, usually considered as a non-perturbing tunneling weak probe, leads to nontrivial effects. This conclusion is supported by numerical renormalization group calculations of the phase diagram of an Anderson impurity coupled to both superconducting and normal-state leads. We obtain this phase diagram for an arbitrary ratio ∆ T K for the first time, which allows us to analyze relevant experimental scenarios, such as parity crossings as well as novel Kondo features induced by the normal lead, as this ratio changes. Spectral functions at finite temperatures and magnetic fields, which can be directly linked to experimental tunneling transport characteristics, show zero-energy anomalies irrespective of whether the system is in the doublet or singlet regime. We also derive the analytical condition for the occurrence of Zeeman-induced fermion-parity switches in the presence of interactions which bears unexpected similarities with the condition for emergent MBSs in nanowires.

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Section: Discussionmentioning

confidence: 99%

Section: Motivation and Introductionmentioning

confidence: 99%

Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

et al. 2015

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“…Nonperturbative treatment beyond the simple SW approach based on the flow equations (corrected version of Ref. [44]) shows sharp but smooth features at the transition point; this issue is, however, beyond our current scope and the refined results will be published elsewhere. For the largest value of U d in the particle-hole symmetric case (black curves in panel a) when the system is close to the π phase for all φ's the agreement between the two methods is nearly perfect.…”

Section: Spectral Function and The Kondo Scalementioning

confidence: 95%

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

et al. 2017

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We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-π) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact Numerical Renormalization Group and Quantum Monte Carlo calculations along with perturbative treatments in terms of the Coulomb repulsion and the hybridization term. Our results address especially the correlation effects reflected in dependencies of various quantities on the local Coulomb interaction strength as well as on the coupling to the normal lead. We quantitatively establish the phase-dependent Kondo temperature log TK (φ) ∝ cos 2 (φ/2) and show that it can be read off from the half-width of the zero-bias enhancement in the Andreev conductance in the doublet phase, which can be experimentally measured by the tunneling spectroscopy.

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“…In this particular regime the Kondo correlations due to the coupling with the normal lead are negligible and we can treat the tunnelling with the normal lead to lowest non-vanishing order. A large body of theoretical work regards the interplay of superconductivity and Kondo physics [60][61][62][63][64][65] . For the subgap transport characteristics of the system, the superconductor can be described by means of an effective Hamiltonian which becomes exact in the regime of infinite superconducting gap.…”

Section: A Quantum-dot Hamiltonianmentioning

confidence: 99%

Finite-frequency noise in a quantum dot with normal and superconducting leads

2015

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We consider a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. We employ a diagrammatic real-time approach to calculate the finite-frequency current noise for subgap transport. The noise spectrum gives direct access to the internal dynamics of the dot. In particular the noise spectrum shows sharp dips at the frequency of the coherent oscillations of Cooper pairs between dot and superconductor. This feature is most pronounced when the superconducting correlation is maximal. Furthermore, in the quantum-noise regime, ω > kBT, µN, the noise spectrum exhibits steps at frequencies equal to the Andreev addition energies. The height of these steps is related to the effective coupling strength of the excitations. The finite-frequency noise spectrum hence provides a full spectroscopy of the system.

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Kondo impurity between superconducting and metallic reservoir: the flow equation approach

Cited by 3 publications

References 21 publications

Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

Finite-frequency noise in a quantum dot with normal and superconducting leads

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