Motivated by recent reports of ambient-pressure superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ films grown on ${\mathrm{LaSrAlO}}_4$, we investigate the superconducting instability in a one-unit-cell (1UC) thin film using ab initio and random-phase approximation techniques. Compared to the high-pressure bulk system, the ratio of interlayer $d_{3z^2-r^2}$ hopping to intralayer $d_{x^2-y^2}$ hopping is suppressed in the 1UC thin film, and the crystal-field splitting of the $e_g$ orbitals is increased. Our calculation indicates that spin-fluctuation-driven pairing correlations are weak for the stoichiometric case at ambient pressure, but increase significantly under hole doping. The leading pairing symmetry is also found to change by hole doping. Specifically, we obtain a leading $d_{x^2-y^2}$ pairing state at moderate hole doping, followed by a $d_{xy}$ state at higher doping. These states are driven by intraband spin-fluctuation scattering within the $\gamma$ hole pocket centered around the $M$ point, and arise primarily from states in the Ni layer farther from the substrate. These results strongly suggest that the thin-film superconducting samples are hole-doped and that pairing in this system predominantly arises in the layer, as opposed to the interlayer pairing in the pressurized bulk system.

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• Multiband superconductivity
• Pairing mechanisms
• Superconductivity
• High-temperature superconductors
• Nickelates
• Strongly correlated systems
• First-principles calculations
• Hubbard model
• Random phase approximation
• Wannier function methods