Slave-spin approach to the Anderson-Josephson quantum dot

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−π transition of the junction. The mean-field theory qualitatively captures the Kondo singlet phase and its competition with superconductivity for weak values of the Bardeen-Cooper-Schrieffer (BCS) gap, including the nontrivial 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.

Source-reported materials — not catalogue approval

Similar papers