Supercurrent and multiple singlet-doublet phase transitions of a quantum dot Josephson junction inside an Aharonov-Bohm ring

TL;DR

This paper investigates a quantum dot Josephson junction within an Aharonov-Bohm ring, revealing complex phase transitions, re-entrant behavior, and the influence of Coulomb interactions on the Josephson current through analytical and numerical methods.

Contribution

It extends the understanding of quantum dot Josephson junctions by analyzing phase transitions and re-entrance phenomena in an interferometric setup using a combination of analytical and functional renormalization group techniques.

Findings

Multiple singlet-doublet phase transitions occur with non-monotonic dependence on coupling strength.

The Josephson current can become negative in the singlet phase due to Coulomb interactions.

Analytical solution for the large gap limit provides insights into the system's behavior.

Abstract

We study a quantum dot Josephson junction inside an Aharonov-Bohm environment. The geometry is modeled by an Anderson impurity coupled to two directly-linked BCS leads. We illustrate that the well-established picture of the low-energy physics being governed by an interplay of two distinct (singlet and doublet) phases is still valid for this interferometric setup. The phase boundary depends, however, non-monotonically on the coupling strength between the superconductors, causing the system to exhibit re-entrance behavior and multiple phase transitions. We compute the zero-temperature Josephson current and demonstrate that it can become negative in the singlet phase by virtue of the Coulomb interaction U. As a starting point, the limit of large superconducting energy gaps \Delta=\infty is solved analytically. In order to tackle arbitrary \Delta<\infty and U>0, we employ a truncated functional renormalization group scheme which was previously demonstrated to give quantitatively reliable results for the quantum dot Josephson problem.