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

TL;DR

This paper investigates the complex sub-gap excitation spectra of double quantum dots coupled to superconductors using NRG, revealing how various parameters influence ground states and spectral features, including quantum phase transitions.

Contribution

The study provides a detailed non-perturbative analysis of the two-impurity Anderson model, highlighting new spectral phenomena and phase transitions in double quantum dot systems.

Findings

Inversion of triplet and singlet states at large hybridization.

Splitting of Shiba doublet states at phase difference and away from half-filling.

Identification of quantum phase transitions associated with doublet ground states.

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.