<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>±</mml:mo> </mml:mrow> </mml:math> pairing symmetry from electron-phonon coupling in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub>

The recently discovered bilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ exhibits superconductivity with a remarkable transition temperature ${T}_{c}\ensuremath{\approx}80$ 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-${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and Ni-${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals are treated equally in both interlayer and intralayer coupling interactions, and (ii) the half-coupling case, where the intralayer coupling involves only the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital, while the interlayer coupling is restricted to the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital. Our calculations reveal that the interlayer coupling favors an $s\ifmmode\pm\else\textpm\fi{}$-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.