The discovery of superconductivity in Ruddlesden-Popper (RP) nickelates has drawn great attention. Many works have been done to study the superconductivity as well as to find more superconducting RP nickelates. However, there is a lack of general understanding regarding the key factors that contribute to the superconductivity of RP nickelates. Here, we systematically study the series of RP nickelates under doping or high-pressure conditions by means of density functional theory plus dynamical mean-field theory. We find that enhanced quasiparticle weights and local spin fluctuation of the $\mathrm{Ni}\text{−}{e}_g$ orbitals are commonly realized by hole doping or high pressure in the known superconducting RP nickelates, suggesting that they are crucial to the superconductivity. We also summarize experimentally synthesized RP nickelates into phase diagrams with local spin moment and local entanglement entropy as parameters, where phases of spin density wave/antiferromagnetism, superconductivity, and Fermi liquid are distinguished. At last, we predict a promising candidate for superconducting RP nickelates, which is constructed in a “bilayer-trilayer” stacking sequence.

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• Phase diagrams
• Spin fluctuations
• Strongly correlated systems
• Transition metal oxides
• Unconventional superconductors
• Density functional theory
• Dynamical mean field theory
• Non-Fermi-liquid theory