Strongly correlated doped hole carriers in the superconducting nickelates: Their location, local many-body state, and low-energy effective Hamiltonian

The families of high-temperature superconductors recently welcomed a new member: hole-doped nickelate ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$ with a $\sim 15\mathrm{K}$ transition temperature. To understand its emergent low-energy behaviors and experimental properties, an immediate key question is whether the superconducting hole carriers reside in oxygen as in the cuprates or in nickel as in most nickelates. We answer this crucial question via a $(\mathrm{LDA}+U)+\mathrm{ED}$ scheme: deriving an effective interacting Hamiltonian of the hole carriers from density functional $\mathrm{LDA}+U$ calculation and studying its local many-body states via exact diagonalization. Surprisingly, distinct from the expected ${\mathrm{Ni}}^{2+}$ spin-triplet state found in most nickelates, the local ground state of two holes is actually a Ni-O spin-singlet state with the second hole greatly residing in oxygen. The emerged eV-scale model therefore resembles that of the cuprates, advocating further systematic experimental comparisons. Tracing the microscopic origin of this unexpected result to the lack of apical oxygen in this material, we proposed a route to increase superconducting temperature and a possible quantum phase transition absent in the cuprates.

Figure 1

Spin majority [(a), (c)] and minority [(b), (d)] band structure of undoped ${\mathrm{NdNiO}}_2$ under FM [(a)(b)] and AFM [(c)(d)] orders from LDA $+$ $U$ calculations, presented (unfolded) in the one-Ni Brillouin zone with relative weight of Ni, Nd, and O atoms shown in red, blue, and green. Note that spin-majority aligned Nd-$f$ orbitals are made transparent to provide a clearer picture, which breaks weakly the symmetry between panels (c) and (d). Detailed comparison near the Fermi energy for AFM-ordered undoped ${\mathrm{NdNiO}}_2$ (e) and 25% doped ${\mathrm{Nd}}_3{\mathrm{SrNi}}_4{\mathrm{O}}_8$ (f) shows that the doped holes reside mainly in O-$p_{//}$ (green) and Ni-$d_{x^2-y^2}$ (red) orbitals.

Figure 2

Comparison of the Hartree-Fock band structures of our four-orbital model [(b), (d)] and those of LDA $+$ $U$ ones [(a), (c)] within the same Ni $d_{x^2-y^2},d_{3z^2-r^2}$ and O $p_{//}$ subspace, under FM [(a), (b)] and AFM [(c), (d)] order. (e), (f) Illustration of outer-shell Wannier orbitals for symmetric $P_s$(e) and antisymmetric $P_a$(f) superposition of O $p_{//}$ orbitals, colored according to the density gradient, from negative (blue) to positive (red).