Fermi surfaces of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.9}$ as seen by angle-resolved photoemission

We have carried out angle-resolved photoemission spectroscopy on single crystals of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.9}$. The crystals were cleaved in situ, under ultrahigh vacuum while the sample stage was cooled to 8 K. By observing the dispersion of the electron energy bands as they cross the Fermi energy, we have mapped the Fermi surfaces. There is reasonable agreement between the experimental results and the predictions of band-structure calculations using the local-density approximation, as well as with positron annihilation experiments. Rather than δ holes, these results indicate that the Fermi surface of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.9}$ encloses 1+δ holes, where δ is the doping level.