Model for low-energy electronic states probed by x-ray absorption in high-Tccuprates

The low-energy electronic states in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ have recently been probed by soft-x-ray-absorption measurements as a function of doping (x) from the insulating well into the metallic (superconducting) regime. A model for understanding and interpreting those spectra is presented. The electronic structure of the active Cu-O planes is represented by an extended three-band Hubbard model whose parameters have been previously derived from quantum-chemical calculations. The essential additional Coulomb interaction between the core hole created in the absorption process and the nearby valence electrons has been included by calculating the necessary on-site and nearest-neighbor core-valence Coulomb parameters. The absorption spectra are calculated using exact-diagonalization techniques for finite clusters. The low-energy electronic structure can be represented within an effective one-band Hubbard model whose parameters are obtained by a mapping from the three-band model. The transition operator for the absorption process as well as the core-hole Coulomb potential are also mapped into the one-band model. The final calculations in the one-band model are performed for the insulator (half filling) and for several excess hole concentrations in the metal. The theoretical and experimental spectra are compared in detail. The calculations accurately account for the observed peak intensities as a function of doping. Important features include the gap between the preedge peaks in the metal, core-hole excitonic effects, and transfer of oscillator strength. In particular, the preedge peak separation is the charge-transfer gap (from the insulator) reduced by the core-hole exciton binding energy. The transfer of oscillator strength between the observed peaks, which is a key signature of the correlated band situation, is analyzed in detail. A doped charge-transfer insulator model for the electronic structure of the cuprates explains the essential features of the x-ray-absorption data.