Numerical sub-gap spectroscopy of double quantum dots coupled to superconductors

Abstract

Double quantum dot nanostructures embedded between two superconducting leads or in a superconducting ring have complex excitation spectra inside the gap which reveal the competition between different many-body phenomena. We study the corresponding two-impurity Anderson model using the non-perturbative numerical renormalization group (NRG) technique and identify the characteristic features in the spectral function in various parameter regimes. At half-filling, the system always has a singlet ground state. For large hybridization, we observe an inversion of excited inter-dot triplet and singlet states due to the level-repulsion between two sub-gap singlet states. The Shiba doublet states split in two cases: a) at non-zero superconducting phase difference and b) away from half-filling. The most complex structure of sub-gap states is found when one or both dots are in the valence fluctuation regime. Doublet splitting can lead to a parity-changing quantum phase transition to a doublet ground state in some circumstances. In such cases, we observe very different spectral weights for the transitions to singlet or triplet excited Shiba states: the triplet state is best visible on the valence-fluctuating dot, while the singlets are more pronounced on the half-filled dot.

14 pages, 14 figures. Final version

References in corpus (22)

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• The Kondo Temperature of SU(4) Symmetric Quantum Dots
• Quantum Monte Carlo study of nonequilibrium transport through a quantum dot coupled to normal and superconducting leads
• Dynamics of capacitively coupled double quantum dots
• Capacitive interactions and Kondo effect tuning in double quantum impurity systems
• Spin-resolved spectra of Shiba multiplets from Mn impurities in MgB_2

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• Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe${}_2$ with spin orbit coupling
• Generalized atomic limit of a double quantum dot coupled to superconducting leads
• Nonlocal Andreev Reflections as a Source of Spin Exchange and Kondo Screening
• Transient effects in double quantum dot sandwiched laterally between superconducting and metallic leads
• Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models
• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
• Effective low-energy models for superconducting impurity systems
• Second Order Perturbation Theory for a Superconducting Double Quantum Dot
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• Superconducting quantum dot and the sub-gap states
• Transport properties of proximitized double quantum dots
• Investigation of the Yu-Shiba-Rusinov states of a multi-impurity Kondo system
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Transient triplet blockade in Andreev junction