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We study the Josephson effect in the multiterminal junction of topologicalsuperconductors. We use the symmetry-constrained scattering matrix approach toderive band dispersions of emergent sub-gap Andreev bound states in amultidimensional parameter space of superconducting phase differences. We finddistinct topologically protected band crossings that serve as monopoles offinite Berry curvature. Particularly, in a four-terminal junction the admixtureof $2\pi$ and $4\pi$ periodic levels leads to the appearance of finite energyMajorana-Weyl nodes. This topological regime in the junction can becharacterized by a quantized nonlocal conductance that measures the Chernnumber of the corresponding bands. In addition, we calculate current-phaserelations, variance, and cross-correlations of topological supercurrents inmultiterminal contacts and discuss the universality of these transportcharacteristics. At the technical level these results are obtained byintegrating over the group of a circular ensemble that describes the scatteringmatrix of the junction. We briefly discuss our results in the context ofobserved fluctuations of the gate dependence of the critical current intopological planar Josephson junctions and comment on the possibility of paritymeasurements from the switching current distributions in multiterminal Majoranajunctions.

Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect