BSE calculations of color center defects in diamond

Colored diamonds are both of fundamental and commercial interest. Several recent efforts have focused on determining the origin of their color. For example, experiments show that the color of blue diamonds is associated with isolated boron impurities\footnote{J.Walker, Rep. Prog. Phys. {\bf 42} 1605 (1979).} while nitrogen impurities are responsible for yellow diamonds. It has previously been shown \footnote{F.Farges \textit{et al.}, Europhysics News {\bf43}, 20 (2012).} that theoretical Bethe-Salpeter Equation (BSE) simulations of boron-doped diamond yield a dark-blue diamond in good agreement with that observed. However, the structure of the nitrogen defects is not well understood. Here we present BSE calculations of the optical response of nitrogen-doped diamonds using relaxed 64-atom unit cells. We focus on N$_x$V$_y$ defect sites, where $x$ is the number of substitutional nitrogen atoms and $y$ is the number of carbon vacancies. We find that the most likely candidates are the N$_3$V$_1$ and N$_2$V$_0$ defects, which show absorption in the 2.5-3.2 eV range, consistent with yellow color. Our results also rule out the N$_1$V$_0$ and N$_4$V$_1$ defect types as possible yellow centers.