Exact diagonalization calculations of hole binding around Ni impurities in Ni-substituted cuprate superconductors
We examine the influence of Ni impurity in cuprates on the distribution of hole carriers by performing numerically exact diagonalization calculations for a model consisting of $\text{Cu}\text{ }3d$, $\text{Ni}\text{ }3d$, and $\text{O}\text{ }2p$ orbitals. Using realistic parameters for the system, we find that a hole is predominantly bound to $\text{O}\text{ }2p$ orbitals around the Ni impurity forming the Zhang-Rice doublet. This imposes strong restrictions on modeling Ni-substituted cuprates. We propose a resonant inelastic x-ray scattering experiment for $\text{Ni}\text{ }K$ edge to confirm hole binding around the Ni impurity.
Abstract In this work we study conditions for guaranteeing the nonnegativity of a discrete-time singular control system. A first approach can be found in the literature for general systems, using the whole coefficient matrices. Also, the particular case of matrices of index 1 has been treated by using a block decomposition and the group-projector of the matrix that gives the singularity to the system. In order to complete this study, an analysis of the nonnegativity of a singular control system for matrices having arbitrary index is done by means of the core–nilpotent decomposition. This technique allows us to reduce the size of the original matrices, improving the results where the whole coefficients are involved.