Effective Hamiltonian for nickelate oxides Nd_{1−x}Sr_{x}NiO_{2}

We derive the effective single-band Hamiltonian in the flat NiO_{2} planes for nickelate compounds Nd_{1−x}Sr_{x}NiO_{2}. We implement the first-principles calculation to study electronic structures of nickelates using the Heyd-Scuseria-Ernzerhof hybrid density functional and derive a three-band Hubbard model for Ni-O pdσ bands of Ni^{+}3d_{x^{2}−y^{2}} and O^{2−}2p_{x/y} orbitals in the NiO_{2} planes. To obtain the effective one-band t-t^{′}-J model Hamiltonian, we perform the exact diagonalization of the three-band Hubbard model for the Ni_{5}O_{16} cluster and map the low-energy spectra onto the effective one-band models. We find that the undoped NiO_{2} plane is a Hubbard Mott insulator and the doped holes are primarily located on Ni sites. The physics of the NiO_{2} plane is a doped Mott insulator, described by the one-band t-t^{′}-J model with t=265meV, t^{′}=−21meV, and J=28.6meV. We also discuss the electronic structure for the self-doping effect and heavy fermion behavior of electron pockets of Nd^{3+}5d character in Nd_{1−x}Sr_{x}NiO_{2}.