Motivated by the recent rapid progress in high-$T_c$ nickelate superconductors, we comprehensively study the physical properties of the alternating bilayer trilayer stacking nickelate ${\mathrm{La}}_7{\mathrm{Ni}}_5{\mathrm{O}}_{17}$. The high-symmetry phase of this material, without the tilting of oxygen octahedra, is not stable at ambient conditions but becomes stable under high pressure, where a small hole pocket ${\gamma }_0$, composed of the $d_{3z^2-r^2}$ states in the trilayer sublattice, appears. This pocket was identified in our previous work for trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ as important to develop superconductivity. Moreover, using random-phase approximation calculations, we find a leading $s^{\pm }$ pairing state for the high-symmetry phase under pressure with similar pairing strength as that obtained previously for the bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ compound, suggesting a similar or higher superconducting transition temperature $T_c$, at the random-phase approximation level. In addition, we find that the dominant magnetic fluctuations in the system driving this pairing state have antiferromagnetic structure both in-plane and between the planes of the top and bottom trilayer and bilayer sublattices, while the middle trilayer is magnetically decoupled.

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• Multiband superconductivity
• Pairing mechanisms
• Superconductivity
• High-temperature superconductors
• Nickelates
• Electron-correlation calculations
• First-principles calculations
• Hubbard model
• Random phase approximation
• Wannier function methods