Quantifying the contributions of Zhang-Rice singlets in the Cu L₃-edge RIXS spectra of doped Bi₂Sr₂CaCu₂O_8+δ with a square-pyramid cluster model

Abstract

We investigate the local electronic structure of Bi₂Sr₂CaCu₂O_8+δ (Bi2212) based on the Cu L₃-edge resonant inelastic X-ray scattering (RIXS) intensity both experimentally and theoretically, across the under-doped (UD), slightly over-doped (OD1) and over-doped (OD2) regimes. The RIXS intensity is examined as a function of incident X-ray polarization (σ and π) and azimuthal angle, as well as the energy transfer that covers from the dd to charge-transfer excitation regime. Doping introduces additional holes that form the local ¹A₁ two-hole ground state, which is dominated by the Zhang-Rice singlet (ZRS) and plays an essential role in the emergence of superconductivity in cuprates. Consequently, the RIXS response of this two-hole ground state serves as a critical probe of the electronic structure in doped cuprates. Utilizing a group theory classification to incorporate the two-hole Coulomb interactions via a Green’s function approach, we analyze the experimental RIXS intensity within a single square-pyramid cluster model. We first derive the RIXS formula for one-hole states and two-hole states, and then we apply a fitting procedure. On the basis of our calculations, we have decomposed the RIXS spectra to disentangle one-hole and two-hole contributions. Through this process, we identified their distinct spectral signatures and determined their doping-dependent weights. The increasing spectral weight of the two-hole states indicates the growing presence of ZRS with doping throughout the studied UD to OD2 regime.

Keywords

Cuprate / RIXS / Zhang-Rice singlet / electronic structure

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