Designing Phase Sensitive Probes of Monopole Superconducting Order

Distinct from familiar $s$-, $p$-, or $d$-wave pairings, the monopole superconducting order represents a novel class of pairing order arising from nontrivial monopole charge of the Cooper pair. In the weak-coupling regime, this order can emerge when pairing occurs between Fermi surfaces with different Chern numbers in, for example, doped Weyl semimetal systems. However, the phase of monopole pairing order is not well-defined over an entire Fermi surface, making it challenging to design experiments sensitive to both its symmetry and topology. To address this, we propose a scheme based on symmetry and topological principles to identify this elusive pairing order through a set of phase-sensitive Josephson experiments. By examining the discrepancy between global and local angular momentum of the pairing order, we can unveil the monopole charge of the pairing order. We demonstrate the proposed probe of monopole pairing order through analytic and numerical studies of Josephson coupling in models of monopole superconductor junctions. This work opens a promising avenue to uncover the unique topological properties of monopole pairing orders and to distinguish them from known pairing orders based on spherical harmonic symmetry.