Josephson effects in the junction formed by \emph{DIII}-class topological and $s$-wave superconductors with an embedded quantum dot

TL;DR

This paper studies Josephson effects in a junction between DIII-class topological and s-wave superconductors with a quantum dot, revealing oscillating currents, fermion parity effects, and coupling-dependent current reversal.

Contribution

It introduces a detailed analysis of Josephson effects in DIII-class topological superconductor junctions with quantum dots, highlighting the role of fermion parity and coupling configurations.

Findings

Josephson current oscillates with 2π period.

Majorana doublets induce finite current at zero phase difference.

Dot-superconductor coupling can reverse the current direction.

Abstract

We investigate the Josephson effects in the junction formed by \emph{DIII}-class topological and $s$-wave superconductors, by embedding a quantum dot in the junction. Three dot-superconductor coupling manners are considered, respectively. As a result, the Josephson current is found to oscillate in $2\pi$ period. Moreover, the presence of Majorana doublet in the \emph{DIII}-class superconductor renders the current finite at the case of zero phase difference, with its sign determined by the fermion parity of such a jucntion. In addition, the dot-superconductor coupling plays a nontrivial role in adjusting the Josephson current. When the $s$-wave superconductor couples to the dot in the weak limit, the current direction will have an opportunity to reverse. The results in this work will be helpful for understanding the transport properties of the \emph{DIII}-class superconductor.