Slave-spin approach to the Anderson-Josephson quantum dot

TL;DR

This paper introduces a slave-spin method to analyze a strongly interacting quantum dot coupled to superconductors, capturing the phase transition and spectral features with improved theoretical insights.

Contribution

The work develops a slave-spin approach combined with diagrammatic techniques to study the quantum dot's phase diagram, spectral properties, and microwave response in the Kondo regime.

Findings

Identifies the 0-π transition in the phase diagram.

Reveals Hubbard bands and a Kondo peak in the spectral function.

Calculates Josephson current and microwave response in the Kondo regime.

Abstract

We study a strongly interacting quantum dot connected to two superconducting leads using a slave-spin representation of the dot. At the mean-field level, the problem maps to a resonant level model with superconducting leads, coupled to an auxiliary spin-1/2 variable accounting for the parity of the dot. We obtain the mean-field phase diagram, showing a transition between a Kondo (singlet) and a local moment (doublet) regime, corresponding to the $0-\pi$ transition of the junction. The mean-field theory qualitatively captures the Kondo singlet phase and its competition with superconductivity for weak values of the BCS gap, including the non-trivial dependence of the Andreev bound states on the interaction, but fails in the doublet regime where it predicts a dot decoupled from the bath. Using diagrammatic techniques and a random phase approximation, we include fluctuations on top of the mean-field theory to describe finite-frequency dynamics of the effective spin variable. This leads to the formation of high-energy Hubbard bands in the spectral function and a coherent Kondo peak with a BCS gap at low energies. We compute the Josephson current and the induced superconducting correlations on the dot. Finally, we evaluate the microwave response in the strongly interacting Kondo regime.