Fractional spin and Josephson effect in time-reversal-invariant topological superconductors

TL;DR

This paper explores how fractional spins in time-reversal-invariant topological superconductors influence the Josephson effect, revealing a quenching of the 0-to-pi transition due to spin singlet formation.

Contribution

It models the impact of fractional spins on Josephson junctions and demonstrates the suppression of the 0-to-pi transition in the topological phase.

Findings

Fractional spins are present at the ends of TRITOPS wires.

The 0-to-pi transition is quenched in the topological phase.

Formation of a spin singlet explains the transition suppression.

Abstract

Time reversal invariant topological superconducting (TRITOPS) wires are known to host a fractional spin hbar/4 at their ends. We investigate how this fractional spin affects the Josephson current in a TRITOPS-quantum dot-TRITOPS Josephson junction, describing the wire in a model which can be tuned between a topological and a nontopological phase. We compute the equilibrium Josephson current of the full model by continuous-time Monte Carlo simulations and interpret the results within an effective low-energy theory. We show that in the topological phase, the 0-to-pi transition is quenched via formation of a spin singlet from the quantum dot spin and the fractional spins associated with the two adjacent topological superconductors.