Superconductivity in La$_4$Ni$_3$O$_{10}$ Under Pressure

Abstract: The discovery of superconductivity (SC) in the trilayer nickelate compound La${4}$Ni$_3$O${10}$ under pressure has generated significant interest. In this work, we propose a trilayer two $E_g$-orbital $t$-$J_{\parallel}$-$J_{\perp}$ model to investigate the microscopic origin of SC in this system. In the strong-coupling regime, each layer is governed by a $t$-$J_{\parallel}$ model with intra-layer antiferromagnetic exchange $J_{\parallel}$, while electrons are allowed to hop between layers, interacting via inter-layer exchange $J_{\perp}$. The inner-layer $3d_{z^2}$-orbital electrons tends to form bonding states with those in the neighboring layers, leading to redistribution of the electron densities. The numerical simulation results indicate that SC is predominantly mediated by the $3d_{z^2}$ orbital, characterized by an intra-layer extended $s$-wave pairing in the outer layers, accompanied by an inter-layer pairing with opposite sign. Furthermore, we find that electron doping enhances SC, while hole doping tends to suppress it. These findings provide new insights into the SC mechanisms of La${4}$Ni$_3$O${10}$ and its sensitivity to charge doping.