Minimal effective model and possible high-$T_{c}$ mechanism for superconductivity of La$_{3}$Ni$_{2}$O$_{7}$ under high pressure

Abstract

The recent discovery of high-$T_{c}$ superconductivity in bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$ under high pressure has stimulated great interest concerning its pairing mechanism. We argue that the weak coupling model from the almost fully-filled $d_{z^{2}}$ bonding band cannot give rise to its high $T_{c}$, and thus propose a strong coupling model based on local inter-layer spin singlets of Ni-$d_{z^{2}}$ electrons due to their strong on-site Coulomb repulsion. This leads to a minimal effective model that contains local pairing of $d_{z^{2}}$ electrons and a considerable hybridization with near quarter-filled itinerant $d_{x^{2}-y^{2}}$ electrons on nearest-neighbor sites. The strong coupling between two components provides a composite scenario to achieve high-$T_{c}$ superconductivity. Our theory highlights the importance of the bilayer structure of superconducting La$_{3}$Ni$_{2}$O$_{7}$ and points out a potential route for the exploration of more high-$T_{c}$ superconductors.Comment: 6 pages, 3 figure