Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots

TL;DR

This paper presents a theoretical study of Andreev bound states in a quantum dot coupled to superconductors, using advanced methods to understand effects of gating and magnetic fields with implications for experimental spectroscopy.

Contribution

It introduces and benchmarks two approaches, fRG and SCABS, for accurately modeling Andreev levels in interacting quantum dots under various conditions.

Findings

Good agreement with exact solutions and NRG calculations

Deepened understanding of Zeeman, gate, and flux effects on Andreev levels

Flexible methods enable extensive parameter space analysis

Abstract

We theoretically investigate the behavior of Andreev levels in a single-orbital interacting quantum dot in contact to superconducting leads, focusing on the effect of electrostatic gating and applied magnetic field, as relevant for recent experimental spectroscopic studies. In order to account reliably for spin-polarization effects in presence of correlations, we extend here two simple and complementary approaches that are tailored to capture effective Andreev levels: the static functional renormalization group (fRG) and the self-consistent Andreev bound states (SCABS) theory. We provide benchmarks against the exact large-gap solution as well as NRG calculations and find good quantitative agreement in the range of validity. The large flexibility of the implemented approaches then allows us to analyze a sizeable parameter space, allowing to get a deeper physical understanding into the Zeeman field, electrostatic gate, and flux dependence of Andreev levels in interacting nanostructures.