Suppressed Josephson phase transition in one parallel double-quantum-dot junction

TL;DR

This study uses numerical methods to analyze how electron correlation and quantum interference affect the Josephson phase transition in a double-quantum-dot junction, revealing suppression of certain phase transitions.

Contribution

It demonstrates that electron correlation suppresses the Josephson phase transition in a parallel double-quantum-dot junction, highlighting the role of nonlocal Cooper pair motion.

Findings

Supercurrent only reaches the $ au'$ phase, not the $ au$ phase, with increased electron correlation.

Detuned dot levels create a $ au'$-phase island in the phase diagram.

Suppression of the Josephson phase transition is linked to nonlocal Cooper pair motion.

Abstract

With the help of the numerical renormalization group method, we theoretically investigate the Josephson phase transition in a parallel junction with one quantum dot embedded in each arm. It is found that in the cases of uniform dot levels and dot-superconductor couplings, the Josephson phase transition will be suppressed. This is manifested as the fact that with the enhancement of the electron correlation, the supercurrent only arrives at its $\pi'$ phase but cannot enter its $\pi$ phase. Moreover, when the dot levels are detuned, one $\pi'$-phase island appears in the phase diagram. Such a result is attributed to the nonlocal motion of the Cooper pair in this structure. We believe that this work can be helpful in understanding the Josephson phase transition modified by the electron correlation and quantum interference.