Do Se vacancies electron dope monolayer FeSe?

Following the discovery of the potentially very high temperature superconductivity in monolayer FeSe we investigate the doping effect of Se vacancies in these materials. We find that Se vacancies pull a vacancy centered orbital below the Fermi energy that absorbs most of the doped electrons. Furthermore we find that the disorder induced broadening causes an effective hole doping. The surprising net result is that in terms of the band structure Se vacancies behave like hole dopants rather than electron dopants. Our results exclude Se vacancies as the origin of the large electron pockets measured by angle resolved photoemission spectroscopy.