Type II t-J model in charge transfer regime in bilayer La\(_3\)Ni\(_2\)O\(_7\) and trilayer La\(_4\)Ni\(_3\)O\(_{10}\)

Abstract

Recent observations of an 80 K superconductor in La\(_3\)Ni\(_2\)O\(_7\) under high pressure have attracted significant attention. Recent experiments indicate that La\(_3\)Ni\(_2\)O\(_7\) may be in the charge transfer regime, challenging the previous models based purely on the Ni \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals. In this study, we propose a low energy model that incorporates doped holes in the oxygen \(p\) orbitals. Given that the parent nickel state is in the \(3d^{8}\) configuration with a spin-one moment, doped hole only screens it down to spin-half, in contrast to the Zhang-Rice singlet in cuprate. We dub the single hole state as Zhang-Rice spin-half and build an effective model which includes three spin-one states (\(d^8\)) and two Zhang-Rice spin-half states (\(d^8 L\)). At moderate pressure around \(20\) GPa, the dominated oxygen orbital is an in-plane Wannier orbital with the same lattice symmetry as the \(d_{x^2-y^2}\) orbital. The resulting model reduces to the bilayer type II t-J model previously proposed in the Mott-Hubbard regime. Notably, the hopping between the in-plane \(p\) orbitals of the two layers is still suppressed. Density matrix renormalization group (DMRG) simulation reveals a pairing dome with the optimal hole doping level at \(x=0.4\sim0.5\), distinct from the hole doped cuprate where optimal doping occurs around \(x=0.19\). Further increasing pressure initially raises the critical temperature (\(T_c\)) until reaching an optimal pressure beyond which the \(p_z\) orbital of oxygen becomes favorable and superconductivity is diminished. This shift from in-plane \(p\) orbital to \(p_z\) orbital may elucidate the experimentally observed superconducting dome with varying pressure. As an extension, we also suggest a trilayer version of the type II t-J model as the minimal model for pressured La\(_4\)Ni\(_3\)O\(_{10}\), which is distinct from the models in the Mott-Hubbard regime.