Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads

Abstract

We derive and apply a general scheme for mapping a setup consisting of a half-filled single level quantum dot coupled to one normal metallic and two superconducting phase-biased leads onto an ordinary half-filled single impurity Anderson model with single modified tunneling density of states. The theory allows for the otherwise unfeasible application of the standard numerical renormalization group and enables to obtain phase-dependent local spectral properties as well as phase-dependent induced pairing and Josephson current. The resulting transport properties match well with the numerically exact continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled normal electrode, the spectral properties can be interpreted in terms of normal-electrode-broadened Andreev bound states with phase-dependent position analogous to the superconducting Anderson model, which coexist in the $\pi$-like phase with a Kondo peak whose phase-dependent Kondo temperature follows the form conjectured previously in Domański et al., Phys.~Rev.~B {\bf 95}, 045104 (2017)

18 pages, 8 figures, submitted to Phys. Rev. B

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• Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs
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• Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
• Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory
• Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions
• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
• Effective low-energy models for superconducting impurity systems
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics
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• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Evolution of the Andreev bands in the half-filled superconducting periodic Anderson model