Modeling Candidate Color Centers in 2D Materials—Hexgonal Boron Nitride

Hexagonal boron nitride (hBN), a promising two-dimensional (2D) material exhibiting single photon emitters (SPEs) favorable for quantum technologies, was recently discovered to exhibit a long-lived coherent spin center operable at room temperature [1]. Known to be carbon-related, this defect center has not yet been definitively characterized. Modeling defects in 2D materials poses new, unresolved challenges to modern theory methods. Standard density functional theory (DFT) methods struggle to accurately model defects in 2D, especially charge state defect levels—due to the charge boundary condition problem—and optical energies—the requisite excited states needed lie formally outside the scope of ground state DFT. These challenges are exacerbated by the large computational expense necessary to eliminate finite-size errors in the supercell calculations. The objective of this study is: (1) to establish a reliable theoretical framework for predicting defects in 2D materials; and (2) apply this new framework to characterize the optoelectronic properties of C-related defects in hBN. The local moment countercharge (LMCC) method straightforwardly adapts to 2D systems [2] and rigorously eliminates charge boundary condition errors that afflict standard jellium-based charge neutralization. To demonstrate this, we compute defect levels (ionization energies with respect to vacuum) for hBN defects that successfully converge to an infinite size limit with proper size-scaling behavior. These results, incidentally, avoid a band gap problem. A newly implemented occupation-constrained DFT (occ-DFT) approach, similarly adapted from its 3D origins [3], computes self-consistent excited state DFT energies at the same computational cost of ground state DFT calculations, and accurately predicts photoluminescence (PL) data. This combined LMCC+occDFT method in the SeqQuest DFT code successfully correlates defect properties with experimental PL measurements, bridging the gap between theoretical predictions and experimental observations in 2D systems. This analysis also highlights several remaining challenges in modeling 2D materials, e.g., the need for sophisticated state-selectivity methods in the self-consistent excited state calculations. While the results provide new insights into the nature of SPEs in hBN, analogous calculations for defects in graphene illustrate additional unresolved challenges for modeling defects in 2D materials. By establishing a tangible synergy between theory and experiment, this research lays the groundwork for engineering SPEs by design in hBN and other 2D materials, facilitating advancements in quantum technologies and also applications in radiation-tolerant microelectronics, accelerating integration of 2D materials into current and future technologies.
[1] Stern, H.L., M. Gilardoni, C., Gu, Q. et al. A quantum coherent spin in hexagonal boron nitride at ambient conditions. Nat. Mater. 23, 1379 (2024).
[2] Schultz, P.A., Charged local defects in extended systems, Phys. Rev. Lett. 84, 1942 (2000).
[3] Schultz, P.A. and Lutz, J.J., Using ground state and excited state density functional theory to decipher 3d dopant defects in GaN, J. Phys.: Condens. Mat. 37, 015502 (2025).
----- Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.