The recent discovery of high-Tc superconductivity in bilayer and trilayer nickelates has ignited intense interest, yet the microscopic origins of their magnetism and pairing remain highly debated. Using first-principles and functional renormalization group calculations, we propose a unified itinerant scenario wherein both superconductivity and spin-density wave (SDW) orders are governed by opposite-mirror-parity scattering [1-3]. In bilayer nickelates, we demonstrate that robust s±-wave superconductivity emerges from cooperative interlayer pairing, driven by competing mirror-odd SDW fluctuations when the dz2 bonding band becomes incipient or crosses the Fermi level [2]. This framework naturally reproduces the observed superconducting dome as a function of pressure and doping in bulk and thin-film systems. In trilayer systems, this same scattering mechanism remarkably accounts for the intriguing SDW state—where SDW is confined to the two outer layers—and generates the anisotropic SDW gap recently observed in ARPES measurements [4]. Furthermore, we reveal that electron-phonon coupling from unique out-of-plane breathing modes cooperates with electronic correlations to enhance Tc [5], while non-local Coulomb interactions unexpectedly promote, rather than suppress, interlayer pairing [6]. Finally, we will discuss potential experimental signatures for detecting these pairing symmetries[7-8]. Ultimately, our findings underscore a unified microscopic scenario for understanding magnetism and superconductivity in pressurized bulk and strained thin-film nickelates from an itinerant perspective.

[1] Y. Gu, C. Le, Z. Yang, X. Wu, and J. Hu, Phys. Rev. B. 111, 174506 (2025).
[2] C. Le, J. Zhan, X. Wu, J. Hu, arXiv: 2501.14665.
[3] X. Wu, T. Xiang, J. Hu, to be sumitted.
[4] J. Yang, … X. Wu, M. Wang, L. Zhao, X. Zhou et al., arXiv:2601.22608.
[5] J. Zhan, Y. Gu, X. Wu, and J. Hu, Phys. Rev. Lett. 134, 136002 (2025).
[6] J. Zhan, C. Le, X. Wu, and J. Hu, arXiv:2503.18877 (npj Quantum Materials accepted).
[7] Z. Zhang, J. Zhan, C. Le, H. C. Po, J. Hu, and X. Wu, arXiv:2512.14544 (2025).
[8] J. Zhan, M. Bejas, A. Schnyder, A. Greco, X. Wu, J. Hu, Chin. Phys. Lett. 43, 020706 (2026).