Current-phase relation and $h/e$-periodic critical current of a chiral Josephson contact between 1D Majorana modes

TL;DR

This paper investigates the unique current-phase relation and $h/e$-periodic critical current in a chiral Josephson contact involving 1D Majorana modes, revealing fractional periodicity and distinctive current behaviors.

Contribution

It introduces a detailed analysis of Josephson effects in topological hybrid structures with chiral Majorana modes, highlighting fractional periodicity and novel current-phase relations.

Findings

Fractional $h/e$-periodic critical current pattern.

Sawtooth-like current-phase relation with spikes.

Distinct behaviors in transparent and tunneling regimes.

Abstract

We explore a long Josephson contact transporting Cooper pairs between 1D charge-neutral chiral Majorana modes in the leads via charged Dirac chiral modes in the normal region. We investigate the regimes of (i) transparent contacts and (ii) tunnel junctions implemented in 3D topological insulator/superconductor/magnet hybrid structures. The setup acts as a SQUID controlled by the magnetic flux enclosed by the chiral loop of the normal region. This chirality leads to the fractional $h/e$-periodic pattern of critical current. The current-phase relation can have sawtooth-like shape with spikes at unusual even phases of $2\pi n$.