Optical Properties and Spin States of Inter-layer Carbon Defect Pairs in Hexagonal Boron Nitride: A First-Principles Study

Abstract: Substitutional carbon defects in hexagonal boron nitride (hBN) are prominent single photon emitters (SPEs), and their potential for spin activity ($S\geq1$) 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$_X$C$_X$). We demonstrate that these C$_X$C$_X$ pairs can exhibit a stable triplet spin state at room temperature when closely spaced (e.g., within 3.5-7.1 {\AA}) across hBN layers. As their separation increases beyond this range (e.g., $>7$ {\AA}), they transition into weakly interacting $S=1/2$ 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$_X$C$_X$ pairs is found to be practically monochromatic and within the visible range. Furthermore, we identify specific C$_B$C$_B$ 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'.