The recent discovery of high-$T_c$ superconductivity in bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under high pressure has stimulated great interest concerning its pairing mechanism. We argue that the weak coupling model from the almost fully filled $d_{z^2}$ bonding band cannot give rise to its high $T_c$, and thus propose a strong coupling model based on local interlayer spin singlets of Ni-$d_{z^2}$ electrons due to their strong on-site Coulomb repulsion. This leads to a minimal effective model that contains local pairing of $d_{z^2}$ electrons and a considerable hybridization with near quarter-filled itinerant $d_{x^2-y^2}$ electrons on nearest-neighbor sites. Their strong coupling provides a unique two-component scenario to achieve high-$T_c$ superconductivity. Our theory highlights the importance of the bilayer structure of superconducting ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and points out a potential route for the exploration of more high-$T_c$ superconductors.

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• Pairing mechanisms
• High-temperature superconductors
• Methods in superconductivity
• Unconventional superconductors