New theoretical method to design quasi-atomic systems in the band gap of semiconductors by combining density functional theory (DFT) and the Hubbard effective Hamiltonian: Applications to alpha boron and to the nitrogen-vacancy center in diamond

Crystal point defects offer one possible pathway towards the solid-state implementation of some quantum applications. Conditions for such applications are the existence of a quasi-atomic system (QAS) in the forbidden band gap. Important additional criteria are the possibility to manipulate the spin state by optical excitations and the possibility to control spin selectivity via shelving states.

In the present work, we combine the calculation of total energy in DFT-HSE06 with constrained occupations of the in-gap energy levels, with an in-house Hubbard model fit on the total energy values to describe the many-body energy states  of the negatively charged nitrogen-vacancy (NV) center in diamond. We show the need to extend the Hubbard model beyond usual interactions for the NV center.

We then propose a new theoretical methodology aimed to design QASs similar to the NV center. We introduce the four concepts of primary defect; under-hybridized interstitial impurity; multiple combinations of n primary defects referred to as n-wise combination; and thermodynamic charging. The effectiveness of the methodology is demonstrated by an application to carbon-based defects in alpha (α) rhombohedral (trigonal) boron.