Doping dependence of the hole distribution in the high-temperature superconductor HgBa$_{2}$CuO$_{4+\delta}$ investigated by X-ray absorption spectroscopy

Using polarization dependent X-ray absorption spectroscopy at the O $K$ and Cu $L$ edges, the symmetry and distribution of the doping-induced states in the simple tetragonal model cuprate superconductor HgBa$_{2}$CuO$_{4+\delta}$ are studied as a function of the effective hole concentration $p$. We find that in the heavily underdoped regime, the doped holes predominantly reside in the planar O 2$p_{\mathrm{x,y}}$ orbitals, with an occupancy that extrapolates linearly to zero at $p_{0} =$ 0 and saturates at $p_{2} \approx $ 0.1. In contrast, holes in the apical O 2$p_{\mathrm{z}}$ orbitals only emerge near the boundary of the superconducting dome at $p_{1}$ $\approx $ 0.05. Similar to the planar holes, these apical O holes also exhibit saturation behavior above $p_{2}$. These observations suggest that the apical O holes might play an important role in the formation of superconductivity, and they imply the existence of an electronic instability as optimal doping is approached.