A unified theory of thin film and bulk bilayer nickelates
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The discovery of bilayer nickelate superconductivity in both pressurized bulk and thin films has drawn enormous attention on their similarity and distinction. Here we provide a unified explanation based on the two-component scenario for a number of key experimental observations reported recently. Our theory predicts two superconducting domes upon electron or hole doping, separated by a valence bond state near $d_{z^2}$ half filling for strong interlayer superexchange coupling $J$, and a single dome across half filling with a lower $T_c$ for weak or moderate $J$. Increasing doping drives the normal state from a Fermi liquid to non-Fermi liquid or weak insulating behaviors, with quasi-linear-in-$T$ scattering rate near optimal $T_c$, while breaking the interlayer valence bonds by oxygen vacancies or chemical substitution simultaneously suppresses the superconductivity and causes local Kondo scattering of $d_{x^2-y^2}$ electrons. These explain the different superconducting transitions and normal states in bulk and thin films, the effect of $d_{z^2}$ hole or electron doping, and the Kondo effect in non-superconducting samples. We propose bulk superconductivity at ambient pressure by doping or reducing the interlayer magnetic coupling and predict even higher $T_c$ upon electron doping.
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