\textit{GW} study of the effect of various defects on the band gap of fluorographene

Recently synthesized fluorographene, fully fluorinated graphene in a chair configuration, is a wide band-gap ($E_{g})$ semiconductor with an experimental optical band gap of $\sim$3 eV. However, first-principles calculations have shown that pristine fluorographene should have E$_{g}$ of 5.4 to 7.5 eV. To explain this discrepancy, we have studied the effect of F vacancies, a Stone-Wales (SW) defect, C single vacancies and C double vacancies on E$_{g}$ of fluorographene using density functional theory and the \textit{GW} approximation. F vacancies and a SW defect are not likely to affect $E_{g}$ of fluorographene, whereas a C single vacancy with a doubly fluorinated C atom, a C double vacancy, and a C double vacancy with two doubly fluorinated C atoms lead to a \textit{GW} band gap of $\sim$4 eV, which is consistent with the optically measured E$_{g}$, and they are energetically more favorable than other C vacancies at a wide range of chemical potential of F ($\mu_{F})$.