Optical properties and spin states of inter-layer carbon defect pairs in hexagonal boron nitride: a first-principles study

Substitutional carbon defects in hexagonal boron nitride (hBN) are prominent single photon emitters (SPEs), and their potential for spin activity (<i>S</i> ≥ 1) is particularly intriguing. While studies have largely focused on intra-layer defects, we employ density functional theory (DFT) to investigate inter-layer dimers of identical carbon species (C_XC_X). We demonstrate that these C_XC_X pairs can exhibit a stable triplet spin state at room temperature when closely spaced (<i>e.g.</i>, within 3.5-7.1 Å) across hBN layers. As their separation increases beyond this range (<i>e.g.</i>, >7 Å), they transition into weakly interacting <i>S</i> = 1/2 pairs, characterized by singlet-triplet degeneracy. This regime is predicted to result in a very small zero-field splitting for the triplet manifold, offering a potential explanation for certain optically detected magnetic resonance (ODMR) signals. The zero-phonon line (ZPL) energy of these inter-layer C_XC_X pairs is found to be practically monochromatic and within the visible range. Furthermore, we identify specific C_BC_B inter-layer configurations exhibiting atypical low-energy phonon replicas due to out-of-plane vibrational coupling, a finding that may clarify the vibronic structure of other hBN emitters, such as the 'yellow emitters'.