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The recent discovery of high-$T_{c}$ superconductivity in bilayer nickelateLa$_{3}$Ni$_{2}$O$_{7}$ under high pressure has stimulated great interestconcerning its pairing mechanism. We argue that the weak coupling model fromthe 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 inter-layerspin singlets of Ni-$d_{z^{2}}$ electrons due to their strong on-site Coulombrepulsion. This leads to a minimal effective model that contains local pairingof $d_{z^{2}}$ electrons and a considerable hybridization with nearquarter-filled itinerant $d_{x^{2}-y^{2}}$ electrons on nearest-neighbor sites.Their strong coupling provides a unique two-component scenario to achievehigh-$T_{c}$ superconductivity. Our theory highlights the importance of thebilayer structure of superconducting La$_{3}$Ni$_{2}$O$_{7}$ and points out apotential route for the exploration of more high-$T_{c}$ superconductors.

Inter-layer valence bonds and two-component theory for high-$T_c$ superconductivity of La$_{3}$Ni$_{2}$O$_{7}$ under pressure