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

Hanbit Oh; Boran Zhou; Ya-Hui Zhang

paper

Type II t-J model in charge transfer regime in bilayer La $_{3}$ Ni $_{2}$ O $_{7}$ and trilayer La $_{4}$ Ni $_{3}$ O $_{10}$

arXiv:2405.00092

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 $3 d^{8}$ 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 $x = 0.4 \sim 0.5$ , 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.

7+10 pages, 3+9 figures, 0+1 table

Type II t-J model in charge transfer regime in bilayer La3​Ni2​O7​ and trilayer La4​Ni3​O10​

Abstract

Type II t-J model in charge transfer regime in bilayer La $_{3}$ Ni $_{2}$ O $_{7}$ and trilayer La $_{4}$ Ni $_{3}$ O $_{10}$