Excited-state geometry relaxation of point defects in monolayer hexagonal boron nitride

Point defects in hexagonal boron nitride (hBN) are often discussed as single-photon emitters for quantum technologies. Understanding the dependence of electronic and optical properties on the geometry might help to identify the atomic structure of the defects and is also crucial in order to make these emitters applicable. Here, we study three defects in a monolayer of hBN, namely, $C_{\text{B}}{V}_{\text{N}}$, $C_{\text{B}}{C}_{\text{N}}$, and $C_{\text{B}}{O}_{\text{N}}$, from an ab initio approach. We use (constrained) density functional theory to obtain optimal geometries of the electronic ground state and the first excited state and then refine quasiparticle energies and optical excitation energies using a $GW$ and Bethe-Salpeter equation (BSE) based approach. All three defect systems host transitions between deep-lying defect states. We find the lowest defect exciton of $C_{\text{B}}{C}_{\text{N}}$ at $\sim 4$ eV and of the other two defects at $\sim 2$ eV with significant Stokes shifts of 0.15 and $0.79\mathrm{eV}$, respectively. Finally, we investigate the effects of the Tamm-Dancoff approximation and show that it can have a significant influence on hBN defect excitons calculated from BSE.