Recently, evidence of superconductivity (SC) has been reported in pressurized ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. Here we study its possible pairing mechanism and pairing symmetry. Through fitting the density-functional-theory band structure, we provide a six-orbital tight-binding model. In comparison with the band structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, the additional nonbonding $d_{z^2}$ band is important to the pairing mechanism here. When the multiorbital Hubbard interactions are included, our random-phase-approximation based study yields an $s^{\pm }$-wave SC. The dominant Fermi-surface nesting with vector ${\mathbf{Q}}_1\approx (\pi ,\pi )$ is between the $\gamma$ pocket contributed by the bonding $d_{z^2}$ band top and the ${\alpha }_1$ pocket contributed by the nonbonding $d_{z^2}$ band bottom, leading to the strongest pairing amplitude and opposite gap signs within the two regimes. The dominant real-space pairing is the interlayer $d_{z^2}$-orbital pairing. This $s^{\pm }$-wave pairing pattern is insensitive to the band details. Upon electron doping, the $T_c$ would increase promptly before the system enters the Néel-ordered spin-density-wave phase.

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• Pairing mechanisms
• Superconducting order parameter
• Superconductivity
• Unconventional superconductors
• Hubbard model
• Random phase approximation