Bistable carbon-vacancy defects in $h$-BN

Single photon emitters in hexagonal boron nitride have been extensively studied recently. Although unambiguous identification of the emitters is still under intense research, carbon related defects are believed to play a vital role for the emitter producing zero-phonon-lines in the range of $1.6$ to $2.2$~eV. In this study, we systematically investigate two configurations of carbon-vacancy defects, VNCB and CNVB, by means of density functional theory calculations. We calculated the reaction barrier energies from one defect to the other to determine relative stability. We find the barrier energies are charge dependent and CNVB could easily transform to VNCB in neutral and positive charge states while it is stable when negatively charged. Formation energy calculations show that the VNCB is the dominant defect over CNVB. However, neither VNCB nor CNVB has suitable fluorescence spectra that could reproduce the observed ones. Our results indicate that the origin of the $1.6$-to-$2.2$-eV emitters should be other carbon-related configurations.