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 Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ with a $\sim$15K transition temperature. To understand its emergent low-energy behaviors and experimental properties, an immediate key question is whether the superconducting hole carriers reside in oxygen as in the cuprates, or in nickel as in most nickelates. We answer this crucial question via a ``(LDA+$U$)+ED'' scheme: deriving an effective interacting Hamiltonian of the hole carriers from density functional LDA+$U$ calculation, and studying its local many-body states via exact diagonalization. Surprisingly, distinct from the expected 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 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.