Mixed singlet and triplet two-hole states in Bi₂Sr₂CaCu₂O_8+δunveiled by cluster modeling of the d-d excitations observed by Cu L₃ Resonant Inelastic X-Ray Scattering

We studied the azimuthal dependence of d-d excitations in Bi₂Sr₂CaCu₂O_8+δ (BSCCO) by Cu L₃-edge Resonant Inelastic X-ray Scattering (RIXS) and analyzed the experimental response with a single cluster model. In the absence of doping, a single hole occupies a square-pyramidal 3d⁹ Cu²⁺ cluster. Upon doping, additional holes generate two-hole states. Utilizing group theory classification to incorporate two-hole Coulomb interactions via a Greens function approach, we calculate the ensuing RIXS intensity of the d-d excitations as a function of polarization (σ and π) and azimuthal angle. The computed RIXS intensity, which agrees with the experimental data on doped BSCCO, has contributions both from a one- and two-hole state. Theoretical modeling of the experimental data of doped BSCCO suggests that the two-hole ground state is best described by a Hund’s triplet mixed with a Zhang-Rice singlet state in all the studied doping regions. Our results highlight the existence of the spin-triplet two-hole state for all doping levels, and Hund’s triplet can even become dominant in the optimally doped and over doped regions.