We study the carbon-dimer defect in a hexagonal boron-nitride $\left(h\text{−}\mathrm{BN}\right)$ monolayer using the $GW$ and Bethe-Salpeter many-body perturbation theories within a finite-size cluster approach. While quasiparticle energies converge very slowly with system size due to missing long-range polarization effects, optical excitations converge much faster, with a $1/R^3$ scaling law with respect to cluster average radius. We obtain a luminescence zero-phonon energy of 4.36 eV, including significant 0.13 eV zero-point vibrational energy and 0.15 eV reorganization energy contributions. Interlayer screening decreases further the emission energy by about 0.3 eV. These results bring support to the recent identification of the substitutional carbon dimer as the likely source of the zero-phonon 4.1 eV luminescence line. Finally, the $GW$ quasiparticle energies are extrapolated to the infinite $h$-BN monolayer limit, leading to a predicted defect highest occupied molecular orbital to lowest unoccupied molecular orbital photoemission gap of 7.6 eV. Comparison with the optical gap yields a very large excitonic binding energy of 3 eV for the associated localized Frenkel exciton.

• Received 27 July 2021
• Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.095201