Resonant Inelastic X-ray Scattering Study of the Model Superconductor HgBa$_2$CuO$_{4+\delta}$

The characteristics of the elementary excitations in high-temperature superconductors (HTSC) and their Mott-insulating parent compounds remain a controversial issue after many years of extensive study by different spectroscopic methods. Energy- and momentum-resolved resonant inelastic x-ray scattering (RIXS) is gaining in importance as a powerful tool in the study of elementary charge excitations in HTSC. We report a RIXS study of charge excitations in the 2 - 8 eV range in the structurally simple compound HgBa$_2$CuO$_{4+\delta}$ at optimal doping ($T_c = 96.5 $ K) at several high-symmetry points in the Brillouin zone. The spectra exhibit a significant dependence on the incident photon energy which we carefully utilize to resolve a multiplet of electron-hole excitations, including an excitation at 2 eV, which was previously observed in undoped parent compounds. The observation of the 2 eV excitation is suggestive of a remnant charge transfer gap in the superconducting phase. Our data are consistent with a relatively weak ($ < 0.5$ eV) dispersion of all excitations.