Nature of empty states in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{x}}$

Angle resolved oxygen K-edge x-ray absorption spectroscopy measurements were performed on single crystals of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.9}$. Measurements were carried out on in situ cleaved crystals at 20 K to minimize the loss of oxygen from the surface region of the samples. It was found that there are two distinct transitions between 526 and 531 eV. The peaks in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.9}$ show strong orientation dependence, as well as energy dispersion of 2 eV. After the sample is heated to room temperature, there is only one peak visible which shows little energy dispersion or orientation dependence. Comparison of the experimental results to a transition-state calculation of the absorption cross section shows good agreement indicating that there are holes of σ symmetry on all Cu-O bonds.