Relevance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Cu</mml:mi><mml:mo>–</mml:mo><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math> multiplet structure in models of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> cuprates
Mi Jiang, Mirko Moeller, Mona Berciu, G. A. Sawatzky
Abstract
We revisit the problem of the spectra of two holes in a ${\mathrm{CuO}}_{2}$ layer, modeled as a $\mathrm{Cu}\text{\ensuremath{-}}3{d}^{8}$ impurity with full multiplet structure coupled to a full O-$2p$ band as an approximation to the local electronic structure of a hole-doped cuprate. Unlike previous studies that treated the O band as a featureless bath, we describe it with a realistic tight-binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-$2p$ band structure. We also find that (i) the ligand O-$2p$ orbitals play an essential role, within this impurity model; (ii) the three-orbital Emery model provides an accurate description for the subspace with $^{1}A_{1}$ symmetry, which includes the ground state in the relevant region of the phase diagram; (iii) this ground state has only $\ensuremath{\sim}50%$ overlap with a Zhang-Rice singlet; (iv) there are other low-energy states, in subspaces with different symmetries, that are absent from the three-orbital Emery model and its one-band descendants. These states play an important role in describing the elementary excitations of doped cuprates.