Effective Hamiltonian for nickelate oxides Nd_1-xSr_xNiO₂

We derive the effective single-band Hamiltonian in the flat NiO2 planes for nickelate compounds Nd1-xSrxNiO2. 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 pd sigma bands of Ni+ 3d(x2- y2) and O2- 2p(x/y) orbitals in the NiO2 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 Ni5O16 cluster and map the low-energy spectra onto the effective one-band models. We find that the undoped NiO2 plane is a Hubbard Mott insulator and the doped holes are primarily located on Ni sites. The physics of the NiO2 plane is a doped Mott insulator, described by the one-band t-t'-J model with t = 265 meV, t' =-21 meV, and J = 28.6 meV. We also discuss the electronic structure for the self-doping effect and heavy fermion behavior of electron pockets of Nd3+ 5d character in Nd1-xSrxNiO2.