Doping evolution of the oxygen $K$-edge x-ray absorption spectra of cuprate superconductors using a three-orbital Hubbard model

We study oxygen $K$-edge x-ray absorption spectroscopy (XAS) and investigate the validity of the Zhang-Rice singlet (ZRS) picture in overdoped cuprate superconductors. Using large-scale exact diagonalization of the three-orbital Hubbard model, we observe the effect of strong correlations manifesting in a dynamical spectral weight transfer from the upper Hubbard band to the ZRS band. The quantitative agreement between theory and experiment highlights an additional spectral weight reshuffling due to core-hole interaction. Our results confirm the important correlated nature of the cuprates and elucidate the changing orbital character of the low-energy quasiparticles, but also demonstrate the continued relevance of the ZRS even in the overdoped region.

Figure 1

(a) Cartoon picture of a Zhang-Rice singlet formed by a copper $3d_{x^2-y^2}$ hole hybridized with a hole on its neighboring oxygen $2p_{x,y}$ orbitals. (b) The Cu${}_8$O${}_{16}$ cluster with periodic boundary conditions considered in the exact diagonalization calculations. (c) Schematic of the oxygen $K$-edge x-ray absorption process, highlighting additional spectral weight reshuffling due to core-hole interaction.

Figure 2

Spectral functions calculated using exact diagonalization on a Cu${}_8$O${}_{16}$ cluster at (a) half-filling, (b) 12.5$\%$, and (c) 25$\%$ hole dopings. The ground state energy of the valence electrons at the corresponding filling is defined as zero energy. The solid and the dashed lines represent the electron occupied and unoccupied states, respectively. The spectra are broadened with a 0.1 eV Lorentizian.

Figure 3

Calculations of oxygen $K$-edge XAS (solid red lines) and IPES measurements of unoccupied oxygen-projected DOS (black dotted lines) at various dopings. The yellow shaded area represents the emergent low-energy ZRS band. The XAS and IPES spectra are lined up in energy by their peak maximum positions.

Figure 4

Doping dependence of the ZRS spectral weight. The La${}_{2-x}$Sr${}_x$CuO${}_4$ (LSCO) XAS data are from Refs. 10 (Chen), 12 (Pellegrin), and 14 (Peets). The XAS theory (red circle) is obtained by integrating the yellow shaded area in Fig. 3. The black circle represents the ZRS weight from the IPES calculation of the unoccupied DOS. Both theory curves are rescaled by normalizing their respective 12.5$\%$ ZRS weight to the straight line suggested by experiment,[14] and the ZRS intensity at $0\%$ doping is defined as zero.