Numerical subgap 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 nonperturbative 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 interdot triplet and singlet states due to the level repulsion between two subgap singlet states. The Shiba doublet states split in two cases: (a) at nonzero superconducting phase difference and (b) away from half-filling. The most complex structure of subgap 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.

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