Fractional spin Josephson effect in topological spin superconductors

TL;DR

This paper investigates the fractional spin Josephson effect in topological spin superconductors, revealing how on-site energies influence the transition between fractional and integer effects and enable charge pumping, offering new detection methods.

Contribution

It introduces a toy model for topological spin superconductors and analyzes the impact of on-site energies on the spin Josephson effect and charge pumping phenomena.

Findings

On-site energies induce a transition between fractional and integer spin Josephson effects.

Non-zero on-site energies enable charge pumping through the spin Josephson junction.

Distinct features of topological spin superconductors are identified, absent in Majorana systems.

Abstract

Topological spin superconductors are $p$-wave spin-triplet exciton insulators whose topological edge modes have been shown to obey non-Abelian braiding statistics. Based on a toy model as the spin counterpart of the Kitaev's chain, we study the spin Josephson effect adopting the $S$-matrix as well as the Green's function method. The on-site energies of these topological edge modes lead to a transition between the fractional and integer spin Josephson effects. Moreover, non-vanishing on-site energies will also induce a charge pump through the spin Josephson junction. These two effects, distinct features of topological spin superconductors and absent in Majorana systems, can be utilized for spin transport detection of topological spin superconductors.