Hole states in ${\mathrm{CuO}}_2$ planes and Cu-O chains of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ probed by soft-x-ray absorption spectroscopy

The symmetry and density of unoccupied states of twin-free ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$ single crystals have been investigated by orientation-dependent x-ray absorption spectroscopy at the O 1s edge, using a bulk-sensitive fluoresence-yield-detection method. In conjunction with earlier results obtained by electron-energy-loss spectroscopy, the relative density of unoccupied states for different oxygen sites has been derived. Comparison with local-density energy-band-structure calculations shows reasonable agreement with the experimental results.