Apical-oxygen holes and their pronounced coupling to phonons in a model high-T_c cuprate

Most theoretical models for the cuprate high-temperature superconductors focus on the electronic and lattice degrees of freedom in the CuO₂ planes. Contrary to this common view, we use X-ray absorption and resonant inelastic X-ray scattering spectroscopies to reveal unusual aspects of the out-of-plane apical-oxygen p_z orbitals in the model tri-layer cuprate superconductor HgBa₂Ca₂Cu₃O_8+x. We find a significant amount of holes in the p_z orbital, which we attribute to the incomplete oxidization of the Hg element. The presence of these holes near the Fermi level may enable appreciable hybridization to the planar electronic states, forming collective electronic and lattice dynamics that are more three-dimensional than commonly thought. In particular, we show that the p_z holes exhibit very strong coupling to lattice vibrations which might contribute to the superconducting pairing.