Type-II <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mtext>−</mml:mtext> <mml:mi>J</mml:mi> </mml:math> model in charge transfer regime in bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Ni</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>7</mml:mn> </mml:msub> </mml:mrow> </mml:math> and trilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:msub> <mml:mi>Ni</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">O</mml:mi> <mml:mn>10</mml:mn> </mml:msub> </mml:mrow> </mml:math>
Hanbit Oh, Boran Zhou, Ya-Hui Zhang
Abstract
Recent observations of an 80 K superconductor in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under high pressure have attracted significant attention. Recent experiments indicate that ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ may be in the charge transfer regime, challenging the previous models based purely on the Ni ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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 the Zhang-Rice doublet and build an effective model which includes three spin-one states $({d}^{8})$ and two Zhang-Rice doublet 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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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 simulation reveals a pairing dome with the optimal hole doping level at $x=0.4--0.5$, 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 ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}$, which is distinct from the models in the Mott-Hubbard regime.