Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure

TL;DR

This paper investigates how phase control in a three-terminal quantum dot system influences the interplay between electron correlations and pairing, revealing phase-dependent Kondo effects and measurable spectroscopic signatures.

Contribution

It provides a comprehensive, numerically exact analysis of the phase-tunable correlation and pairing effects in a Josephson-coupled quantum dot with a normal lead, including experimental implications.

Findings

Phase-dependent Kondo temperature scales as cos^2(φ/2).

Zero-bias conductance peak width reveals Kondo temperature.

Correlation effects significantly influence spectral and transport properties.

Abstract

We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-$\pi$) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact Numerical Renormalization Group and Quantum Monte Carlo calculations along with perturbative treatments in terms of the Coulomb repulsion and the hybridization term. Our results address especially the correlation effects reflected in dependencies of various quantities on the local Coulomb interaction strength as well as on the coupling to the normal lead. We quantitatively establish the phase-dependent Kondo temperature $\log T_{K}(\phi)\propto\cos^{2}(\phi/2)$ and show that it can be read off from the half-width of the zero-bias enhancement in the Andreev conductance in the doublet phase, which can be experimentally measured by the tunneling spectroscopy.