Changes of Kondo effect in the junction with DIII-class topological and $s$-wave superconductors

TL;DR

This paper investigates how the Kondo effect is altered in a Josephson junction involving DIII-class topological and s-wave superconductors, revealing unique correlation modes and the impact of topological class on these phenomena.

Contribution

It introduces a detailed analysis of the Kondo effect modifications in DIII-class topological superconductor junctions, highlighting the role of quantum dot correlations and topological class distinctions.

Findings

Quantum dot occupation induces Kondo and singlet-triplet correlations.

DIII-class topological superconductor degenerates into D-class when time-reversal symmetry is broken, eliminating certain correlations.

The topological class significantly influences the Kondo effect and Josephson current behavior.

Abstract

We discuss the change of the Kondo effect in the Josephson junction formed by the indirect coupling between a one-dimensional \emph{DIII}-class topological and s-wave superconductors via a quantum dot. By performing the Schrieffer-Wolff transformation, we find that the single-electron occupation in the quantum dot induces various correlation modes, such as the Kondo and singlet-triplet correlations between the quantum dot and the $s$-wave superconductor and the spin exchange correlation between the dot and Majorana doublet. Moreover, it plays a nontrivial role in modifying the Josephson effect, leading to the occurrence of anisotropic and high-order Kondo correlation. In addition, due to the quantum dot in the Kondo regime, extra spin exchange correlations contribute to the Josephson effect as well. Nevertheless, if the \emph{DIII}-class topological superconductor degenerates into \emph{D}-class because of the destruction of time-reversal invariance, all such terms will disappear completely. We believe that this work shows the fundamental difference between the \emph{D}- and \emph{DIII}-class topological superconductors.