Universal spin-triplet superconducting correlations of Majorana fermions

TL;DR

This paper demonstrates that Majorana fermions on topological superconductor boundaries universally exhibit spin-triplet superconducting correlations, leading to distinctive spin-dependent transport phenomena and offering a new way to detect and manipulate Majorana fermions.

Contribution

It reveals the universal spin-triplet nature of Majorana fermions' superconducting correlations and proposes a novel detection method via current-phase relations in Josephson junctions.

Findings

Majorana fermions induce only spin-triplet superconducting correlations.

Resonant Andreev reflection occurs exclusively in spin-triplet channels.

Unique current-phase relation serves as a signature for Majorana fermions.

Abstract

We establish that Majorana fermions on the boundary of topological superconductors have only spin-triplet superconducting correlations independent of whether the bulk superconducting gap is spin singlet or triplet. This is universal for time-reversal broken (respected) topological superconductors (TSCs) with an odd number of (pairs of) Majorana fermions on the boundary. Consequently, resonant Andreev reflection induced by Majorana fermions only occurs in spin-triplet channels and always injects spin-triplet Cooper pairs into the leads. This spin-triplet condensate results in a spin-orbit coupling (SOC) controlled oscillatory critical current without a $0$-$\pi$ transition in the TSC/SOC-semiconductor/TSC Josephson junction. The observation of this unique current-phase relation can serve as the definitive signal for Majorana fermions. Our study shows a technique for manipulating Majorana fermions based on their spin-triplet superconducting correlations.