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 $\ensuremath{\sim}15\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ 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 cuprates or nickel most nickelates. We answer this crucial via $(\mathrm{LDA}+U)+\mathrm{ED}$ scheme: deriving effective interacting Hamiltonian from density functional $\mathrm{LDA}+U$ calculation studying local many-body states exact diagonalization. Surprisingly, distinct expected ${\mathrm{Ni}}^{2+}$ spin-triplet state found nickelates, ground two holes actually Ni-O spin-singlet second greatly residing oxygen. emerged eV-scale model therefore resembles that cuprates, advocating further systematic comparisons. Tracing microscopic origin unexpected result to lack apical material, we proposed route increase temperature possible quantum phase absent cuprates.