The all-electron $GW$ approximation energy band gap of bulk hexagonal boron nitride is shown to be of indirect type. The resulting computed in-plane polarized optical spectrum, obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function, is in excellent agreement with experiment and has a strong anisotropy compared to out-of-plane polarized spectrum. A detailed analysis of the excitonic structures within the band gap shows that the low-lying excitons belong to the Frenkel class and are tightly confined within the layers. The calculated exciton binding energy is much larger than that obtained by Watanabe et al. [Nat. Mater. 3, 404 (2004).] based on a Wannier model assuming $h\mathrm{\text{−}}\mathrm{BN}$ to be a direct-band-gap semiconductor.

• Received 11 March 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.026402