Symmetry Principles for Phase-Sensitive Probes of Monopole Superconducting Order

Monopole superconducting order is a novel class of topological pairing order which arises when the Cooper pair possesses a nontrivial monopole charge in momentum space. The pairing order cannot be well-defined over an entire Fermi surface and is described by the so-called monopole harmonic functions. Such pairing is realizable in, for example, a doped Weyl semimetal. We explore the potential identification of the exotic pairing order based on a set of phase-sensitive Josephson junctions. Using Green's functions, we derive a form of the leading-order Josephson coupling between a monopole superconductor and other known superconductors. Furthermore, by considering junctions with different relative orientations to the principal rotational axis along which the pairing gap nodes appear, we establish the general symmetry selection rules that can unveil the pair monopole charge both analytically and numerically.