Symmetry-Based Microscopic Theory of the Unconventional Pairing Mechanism in La$_5$Ni$_3$O$_{11}$

Abstract

Recent experiments report high-temperature superconductivity in the hybrid nickelate $\mathrm{La}_5\mathrm{Ni}_3\mathrm{O}_{11}$, which is composed of alternating stacks of bilayer $\mathrm{La}_3\mathrm{Ni}_2\mathrm{O}_7$ and monolayer $\mathrm{La}_2\mathrm{NiO}_4$. However, the superconducting transition temperature $T_c \approx 64~\mathrm{K}$ for $\mathrm{La}_5\mathrm{Ni}_3\mathrm{O}_{11}$ is remarkably lower than the $80~\mathrm{K}$ observed for pressurized $\mathrm{La}_3\mathrm{Ni}_2\mathrm{O}_7$. Thus, an unified microscopic theory is required to address the difference in the pairing mechanisms between these systems. Here, we develop a phenomenological symmetry-based approach to systematically analyze the low-energy physics in $\mathrm{La}_5\mathrm{Ni}_3\mathrm{O}_{11}$, which is obtained by a charge self-consistent density functional theory plus dynamical mean-field theory method. We show that the superconductivity in $\mathrm{La}_5\mathrm{Ni}_3\mathrm{O}_{11}$ exhibits a two-gap nature, consisting of a leading interlayer pairing between the $d_{z^2}$ orbitals and a subleading intralayer pairing between the $d_{x^2-y^2}$ orbitals. The reduction of $T_c$ can be attributed to the diminished contribution of the interlayer pairing, as reflected by the hopping parameter ratio $|t_{\perp}^z/t_{\parallel}^{x}|$. Base on this unified picture, we discuss the possible pairing mechanism and the role of $γ$ pocket for the superconductivity in the bilayer NiO$_2$ planes of nickelate superconductors.