Thermodynamic stability and optical properties of C-doping-induced defects in hexagonal boron nitride as potential single-photon emitters

Quantum information technologies have triggered enormous interest in single-photon emitters (SPEs), such as local defects in wide-band-gap semiconductors. Recently, visible single-photon emission was observed in carbon-doped hexagonal boron nitride (h-BN), yet the structure giving rise to the emission has not been unambiguously identified. Further progress in the rational design of SPEs requires a deep insight into all the ground-state properties, the electronic structure of the defects in question, and their relationship with the optical properties. To this end, we apply state-of-the-art computational methods to evaluate the stability and optical properties of defects that can be responsible for the above-mentioned experimental findings. For our analysis, we select seven possible C-based defects: (i) C substitutes B $({\mathrm{C}}_{\mathrm{B}})$, (ii) C substitutes N $({\mathrm{C}}_{\mathrm{N}})$, (iii) C substitutes N and nearest B and N are interchanged $({\mathrm{C}}_{\mathrm{N}}{\mathrm{N}}_{\mathrm{B}})$, (iv) C substitutes N and there is a nearby B vacancy $({V}_{\mathrm{B}}{\mathrm{C}}_{\mathrm{N}})$, and (v) three different configurations of ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}$ (C substitutes B and a nearby N vacancy). We perform calculations of the electronic structure using the linear response approach ($GW$ method), followed by finding the solution to the Bethe-Salpeter equation to obtain the excitation spectra of dynamically stable defects. Our density-functional-theory-based calculations of the optimized geometries and their \ensuremath{\Gamma}-point phonon frequencies reveal that ${V}_{\mathrm{B}}{\mathrm{C}}_{\mathrm{N}}$ is dynamically unstable and undergoes a transformation to one corrugated ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}$ structure. Likewise, the flat ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}$ (with ${C}_{2\mathrm{v}}$ symmetry) lies on a very shallow and anharmonic minimum that would also relax toward the corrugated ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}$ structure. Clearly, our results demonstrate how important is to attest to the dynamical stability of any proposed structure. Upon comparing our results of the considered defects with the reported experimental SPE spectra, we show that only the ${\mathrm{C}}_{\mathrm{N}}$ defect has an excitation spectrum fitting the conditions for the observed single-photon emission. Importantly, this defect is found to be the most thermodynamically stable among those under consideration.