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

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