Electronic Structure, Magnetic and Pairing Tendencies of Alternating Single-layer Bilayer Stacking Nickelate La${}_5$Ni${}_3$O${}_{11}$ Under Pressure

Nickelates have continued to surprise since their unconventional superconductivity was discovered. Recently, the layered nickelate La${}_5$Ni${}_3$O${}_{11}$ with hybrid single-layer and bilayer stacking showed superconductivity under high pressure. This compound combines features of La${}_2$NiO${}_4$ and La${}_3$Ni${}_2$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. Increasing pressure suppresses these modes and causes ``charge transfer’’ between the single-layer and bilayer sublattices, 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 La${}_5$Ni${}_3$O${}_{11}$ from other nickelate superconductors discovered so far and the high-$T_c$ cuprates. We also discuss both similarities and differences between La${}_5$Ni${}_3$O${}_{11}$ and other hybrid stacking nickelates.