The coexistence of superconductivity and other ordered states is an important topic in condensed matter physics. Superconductivity coexisting with ferromagnetic [1] or antiferromagnetic [2] order has been extensively studied. In contrast, superconducting states coexisting with odd-parity magnetic multipole order have not been clarified both theoretically and experimentally.

Recent NMR measurements on CeRh₂As₂ have suggested the coexistence of superconductivity with a magnetic monopole order, in which magnetic moments are oriented oppositely between sublattices [3]. In such systems, strong correlation effects are expected to play a crucial role. However, previous studies of superconductivity in odd-parity magnetic multipole states have been based on mean-field approximations assuming an attractive interaction for Cooper pairing [4].

In this study, we investigate superconductivity incorporating strong correlation effects using a bilayer Hubbard model with sublattice degrees of freedom. In this model, magnetic monopole fluctuations arising from quantum geometric effects at Dirac points—recently attracting significant attention [5,6]—become dominant. We introduce magnetic monopole order into this model and analyze its impact on magnetic and superconducting properties using the random phase approximation and Eliashberg theory.

References:

[1] Dai Aoki et al., J. Phys. Soc. Jpn. 88, 022001 (2019).

[2] Ludovic Howald et al., Sci. Rep. 5, 12528 (2015).

[3] Shiki Ogata et al., Phys. Rev. B 110, 214509 (2014).

[4] Shuntaro Sumita and Youichi Yanase, Phys. Rev. B 93, 224507 (2016).

[5] Kudo Kanta and Youichi Yanase, arXiv:2505.20907 (2025).

[6] Kosuke Nogaki and Youichi Yanase, arXiv:2510.24289 (2025).