Nickelates have continued to surprise since their unconventional superconductivity was discovered. Recently, the layered nickelate ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ with hybrid single-layer and bilayer stacking showed superconductivity under high pressure. This compound combines features of single-layer ${\mathrm{La}}_2{\mathrm{NiO}}_4$ and bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, but its pairing mechanism remains to be understood. Motivated by this finding, here we report a comprehensive theoretical study of this system. Our density functional theory calculations reveal that the undistorted P4/mmm phase without pressure is unstable due to three distortion modes. As pressure increases, these modes are suppressed, leading to the high-symmetry P4/mmm phase without ${\mathrm{NiO}}_6$ octahedron tilting. Moreover, the “charge transfer” between the single-layer and bilayer sublattices was observed, leading to hole doping in the single-layer blocks. Our random-phase approximation calculations indicate a leading $d_{x^2-y^2}$-wave pairing state that arises from spin-fluctuation scattering between Fermi surface states mainly originating from the single-layer blocks and additional weaker contributions from the bilayer blocks. These spin fluctuations could be detected by inelastic neutron scattering as a strong peak at $\mathbf{q}=(\pi ,\pi )$. Our findings distinguish ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ from other nickelate superconductors discovered so far and the high-$T_c$ cuprates. We also discuss both similarities and differences between ${\mathrm{La}}_5{\mathrm{Ni}}_3{\mathrm{O}}_{11}$ and other hybrid stacking nickelates.

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