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Lateral Josephson effect on the surface of Co$_3$Sn$_2$S$_2$ magnetic Weyl semimetal

We experimentally study lateral electron transport between two 5~$μ$m spaced superconducting indium leads on a top of magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$. For the disordered magnetic state of Co$_3$Sn$_2$S$_2$ crystal, we only observe the Andreev reflection in the proximity of each of the leads, which is indicative of highly transparent In-Co$_3$Sn$_2$S$_2$ interfaces. If the sample is homogeneously magnetized, it demonstrates well-developed anomalous Hall effect state. In this regime we find the Josephson current that takes place even for 5~$μ$m long junctions and shows the unusual magnetic field and temperature dependencies. As a possible reason for the results obtained, we discuss the contribution to the proximity-induced spin-triplet Josephson current from the topologically protected Fermi-arc states on the surface of Co$_3$Sn$_2$S$_2$.