Prediction of $s^{\pm }$-wave superconductivity enhanced by electronic doping in trilayer nickelates La${}_4$Ni${}_3$O${}_{10}$ under pressure

Abstract

Motivated by the recently reported signatures of superconductivity in trilayer La${}_4$Ni${}_3$O${}_{10}$ under pressure, we comprehensively study this system using {\it 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 $s^{\pm }$-wave channel due to partial nesting between the {\bf M}=$(\pi ,\pi )$ centered pockets and portions of the Fermi surface centered at the {\bf $\Gamma$}=$(0,0)$ point. With changing electronic density $n$, the $s^{\pm }$ instability remains leading and its pairing strength shows a dome-like behavior with a maximum around $n=4.2$ ($\sim 6.7\%$ 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${}_7$ may $not$ originate from a trilayer- and single-layer structure. Furthermore, we predict an interesting spin-density-wave state in La${}_4$Ni${}_3$O${}_{10}$ with an in-plane ($\pi$, $\pi$) order and antiferromagnetic coupling between the top and bottom Ni layers, while the middle layer has spin zero.

Main text with 6 pages and 4 figures plus SM with 4 pages and 5 figures

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Cited by in corpus (37)

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• Sensitive dependence of pairing symmetry on Ni-$e_g$ crystal field splitting in the nickelate superconductor La${}_3$Ni${}_2$O${}_7$
• The $s^{\pm }$-Wave Superconductivity in the Pressurized La${}_4$Ni${}_3$O${}_{10}$
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• Magnetic phase diagram of a two-orbital model for bilayer nickelates varying doping
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• DFT+DMFT study of correlated electronic structure in the monolayer-trilayer phase of La${}_3$Ni${}_2$O${}_7$
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• $t$-$J$ model for strongly correlated two-orbital systems: Application to bilayer nickelate superconductors
• Superconductivity in La${}_4$Ni${}_3$O${}_{10}$ Under Pressure
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