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Description
Multiterminal Josephson junctions are of interest both as probes of the topological properties of the superconducting leads and as synthetic topological matter. Using the superconducting phases of the terminals in n-terminal Josephson junctions as variables, one may realize topological band structures in d = n-1 dimensions. For example, it has been shown that a 4-terminal junction may realize the analog of a Weyl semimetal, whereas a 3-terminal junction may realize the analog of a Chern insulator. Extending the analogy to more terminals opens the possibility of realizing topological phases in arbitrary dimensions, not accessible in real materials. As the superconducting phases act as “anomalous” variables, the symmetry-based classification of topological phases in multiterminal junctions differs from the usual table. Here we classify possible phases and provide an example for a gapped 3-dimensional topological phase characterized by a Z2-invariant in symmetry class C using 5-terminal junctions.