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Strongly correlated superconductors provide a fertile platform for unconventional pairing mediated by spin and multipole fluctuations. Recently, the quantum geometry of Bloch wave functions has emerged as another key ingredient controlling electronic instabilities [1]. However, how strong correlations, multipole physics, superconductivity, and quantum geometry cooperate in real materials remains largely unexplored.
CeRh$_2$As$_2$ is an ideal system for addressing this issue. This locally noncentrosymmetric heavy-fermion superconductor exhibits two superconducting phases, suggesting competition between even- and odd-parity superconducting states [2]. NMR/NQR measurements have reported signatures of magnetic monopole order inside the superconducting phase, indicating the importance of odd-parity multipole degrees of freedom [3,4]. In addition, applied pressure significantly modifies the superconducting phase diagram and appears to bring the even- and odd-parity superconducting states close in stability [5,6], a behavior that cannot be captured by a simplified bilayer model [7,8]. These facts call for a realistic microscopic theory incorporating both strong correlations and material-specific electronic structure.
We construct a realistic Dirac-Anderson model for CeRh$_2$As$_2$ based on the low-energy electronic structure revealed by ARPES [9-11] and DFT+$U$ calculations [12]. We show that the quantum geometry of the $f$-electron Dirac band promotes ferroic magnetic monopole fluctuations through a mechanism distinct from the conventional density-of-states-driven Stoner scenario. By solving the linearized Eliashberg equation, we find parity-competitive superconducting states with dominant spin-triplet character associated with the Dirac band.
We further find that electron correlation effects renormalize this quantum-geometric monopole instability and modify the balance between even- and odd-parity superconductivity. This provides a natural interpretation of the pressure evolution of the superconducting phase diagram: pressure suppresses correlation-induced renormalization and brings the two superconducting states closer to degeneracy. Our results identify CeRh$_2$As$_2$ as a material platform where strong correlations, multipole physics, and quantum geometry cooperate to realize parity-competitive unconventional superconductivity [13].
[1] T. Kitamura, A. Daido, and Y. Yanase, Appl. Phys. Lett. 128, 130501 (2026).
[2] S. Khim et al., Science 373, 1012 (2021).
[3] M. Kibune et al., Phys. Rev. Lett. 128, 057002 (2022).
[4] S. Ogata et al., Phys. Rev. B 110, 214509 (2024).
[5] H. Siddiquee et al., Phys. Rev. B 108, L020504 (2023).
[6] K. Semeniuk et al., Phys. Rev. B 110, L100504 (2024).
[7] T. Yoshida, M. Sigrist, and Y. Yanase, Phys. Rev. B 86, 134514 (2012).
[8] K. Nogaki and Y. Yanase, Phys. Rev. B 106, L100504 (2022).
[9] X. Chen et al., Phys. Rev. X 14, 021048 (2024).
[10] B. Chen et al., Phys. Rev. B 110, L041120 (2024).
[11] Y. Wu et al., Chin. Phys. Lett. 41 097403 (2024).
[12] J. Ishizuka, K. Nogaki, M. Sigrist, and Y. Yanase, Phys. Rev. B 110, L140505 (2024).
[13] K. Nogaki and Y. Yanase, Phys. Rev. B 113, 214506 (2026).