The recently discovered bilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ exhibits superconductivity with a remarkable transition temperature $T_c\approx 80$ K under applied pressures above 14.0 GPa. This discovery of a new family of high-temperature superconductors has garnered significant attention in the condensed matter physics community. In this work, we assume this high-temperature superconductor is mediated by phonons and investigate the pairing symmetry in two distinct models: (i) the full-coupling case, where the Ni-$d_{x^2-y^2}$ and Ni-$d_{3z^2-r^2}$ orbitals are treated equally in both interlayer and intralayer coupling interactions, and (ii) the half-coupling case, where the intralayer coupling involves only the $d_{x^2-y^2}$ orbital, while the interlayer coupling is restricted to the $d_{3z^2-r^2}$ orbital. Our calculations reveal that the interlayer coupling favors an $s\pm$-wave superconducting state, whereas the intralayer coupling promotes an $s++$-wave symmetry. Additionally, we discuss the implications of pair-hopping interactions on the superconducting properties. These findings provide valuable insights into the pairing mechanisms and symmetry of this newly discovered high-temperature superconductor.

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• Electron-phonon coupling
• Electronic structure
• Pairing mechanisms
• Superconducting gap
• Nickelates
• BCS theory