Prediction of s^{±}-Wave Superconductivity Enhanced by Electronic Doping in Trilayer Nickelates La_{4}Ni_{3}O_{10} under Pressure.

Motivated by the recently reported signatures of superconductivity in trilayer La_{4}Ni_{3}O_{10} under pressure, we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni d_{3z^{2}-r^{2}} orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p_{z} orbitals inducing a "trimer" lattice in La_{4}Ni_{3}O_{10}, analogous to the dimers of La_{3}Ni_{2}O_{7}. The Fermi surface consists of three electron sheets with mixed e_{g} orbitals, and a hole and an electron pocket made up of the d_{3z^{2}-r^{2}} orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s^{±}-wave channel due to partial nesting between the M=(π,π) centered pockets and portions of the Fermi surface centered at the Γ=(0,0) point. With changing electronic density n, the s^{±} instability remains leading and its pairing strength shows a domelike behavior with a maximum around n=4.2 (∼6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La_{3}Ni_{2}O_{7}, correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T_{c} superconductivity of La_{3}Ni_{2}O_{7} does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La_{4}Ni_{3}O_{10} with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.