Energy Levels and Spin States of Open-Shell Quantum Defects from the Spin-Flip Bethe-Salpeter Approach

Open-shell systems, including molecules and defects, are interesting platforms for spin physics and quantum information, but their multi-determinantal states are difficult to handle with conventional first-principles calculations. A solution is the spin-flip approach from quantum chemistry: the ground and excited states are considered as spin-flipping excitations of a single-determinant high-spin reference state. By analogy to spin-flip time-dependent density-functional theory (SF-TDDFT), we introduce spin-flip to the GW/Bethe-Salpeter approach (GW/BSE) for applicability to solids [1]. We implemented this spin-flip BSE approach in the BerkeleyGW code, and demonstrated success on torsion of the ethylene molecule as a benchmark, as well as quartet-doublet splitting in the CuO molecule. Moving to defects, we find good results also for the diamond NV⁻ center and SiV⁰ defects, showing promise for accurate calculations of defects in solids, without the need for embedding or construction of an effective Hamiltonian. We analyze the significance and subtleties of applying GW corrections in this scheme. Through calculations of the S² operator on our states [2], we can determine the spin character, and we find only small spin contamination in our results, unlike in typical SF-TDDFT calculations. Our SF-BSE approach can also be straightforwardly generalized to provide forces, using our BSE excited-state forces formalism. We are also applying SF-BSE to the Si G-center and a Co substitution for S in monolayer WS₂ [3]. This method offers new capabilities for characterizing the energies and spins of the energy levels of defects and identifying promising new defect systems.

[1] Bradford A. Barker and David A. Strubbe, “Spin-flip Bethe-Salpeter equation approach for ground and excited states of open-shell molecules and defects in solids,” arXiv:2207.04549 (2022).
[2] Bradford A. Barker, Arabi Seshappan, and David A. Strubbe, “Computation of the expectation value of the spin operator S² for the Spin-Flip Bethe-Salpeter Equation,” Electron. Struct. 6, 027001 (2024).
[3] John C. Thomas et al., “A substitutional quantum defect in WS₂ discovered by high-throughput computational screening and fabricated by site-selective STM manipulation,” Nat. Commun. 15, 3556 (2024).