Interband Transitions in La$_{2-x}$Sr$_{x}$CuO$_{4}$ observed by Resonant Inelastic X-Ray Scattering

Resonant inelastic x-ray scattering measures the energy and momentum dependence of electronic excitations, whose probabilities are resonantly enhanced, in this study, by utilizing hard x-rays at the Cu K-edge absorption energy. Three main features in the resonant inelastic x-ray scattering spectrum of La$_{2-x}$Sr$_{x}$CuO$_{4}$ were observed to develop as the doping x increased from the underdoped to the overdoped region of the high-temperature superconductor phase diagram. Measured at the zone-boundary momentum transfer ($\pi $ 0), the spectra consist of three main peaks: one peak below an isosbestic point at 2.2 eV which strengthens at high doping, and two broad peaks above - one at 3.3 eV increasing in energy and decreasing in intensity, and the other stationary at higher energy. Taking a cue from existing band structure calculations, these peaks are interpreted as the transitions between stationary bands of non-bonding Oxygen, a Zhang-Rice singlet type band at the Fermi level, and the upper Hubbard band. These transitions are also discussed in the context of existing angle-resolved photoemission data.