Arnaud, Lebègue, Rabiller, and Alouani Reply: In a recent Letter [1], we have shown that h-BN is a large gap indirect insulator with a minimum direct band gap of 6.47 eV and the absorption spectra is dominated by strong excitonic effects evidenced by the large calculated binding energy of 0.72 eV. In order to get a converged dielectric function with a reasonable number of k points, we used a slightly shifted 12 12 8 mesh grid. The advantage of this shifted k-point grid is that it avoids degenerate energies located at high symmetry planes, and the disadvantage is that it breaks the symmetry of the lattice and hence slightly lifts the degeneracy of the excitons. Indeed, we obtained four low-lying excitonic structures, respectively, located at 5.75, 5.78, 5.82, and 5.85 eV with a lower oscillator strength for the first two excitons than for the last two excitons. Our calculations for a nonshifted grid show that the first two structures merge into a single nonoptically active exciton (dark exciton) at 5.83 eV and that the last two structures at 5.85 eV are degenerate with

The calculated quasiparticle band structure of bulk hexagonal boron nitride using the all-electron GW approximation shows that this compound is an indirect-band-gap semiconductor. The solution of the Bethe-Salpeter equation for the electron-hole two-particle Green function has been used to compute its optical spectra and the results are found in excellent agreement with available experimental data. A detailed analysis is made for the excitonic structures within the band gap and found that the 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[1] using a Wannier model to interpret their experimental results and assuming that h-BN is a direct-band-gap semiconductor.PACS numbers: 71.15. Mb, 71.35.Cc, Hexagonal boron nitride (h-BN) is one of the most anisotropic layer compounds and represents an interesting quasi-two-dimensional insulator analog to semimetallic graphite. Due to its high thermal stability, h-BN is a widely used material in vacuum technology. It has been employed for microelectronic devices [2], for x-ray lithography masks [3], and as a wear-resistant lubricant [4]. The interest in h-BN has been renewed by the possibility of preparing boron nitride nanotubes that are far more resistant to oxidation than carbon nanotubes and therefore suited to high temperature applications. As their band gaps are predicted to be weakly dependent on helicity and tube diameter [5,6], unlike tubes made of carbon, it has the potential of revolutionizing the electronics industry. To understand the quasiparticle properties of BN nanotubes one has first to have a complete understanding of the electronic and optical properties of bulk h-BN since BN nanotubes can be viewed as a rolled up BN sheets.Despite the large number of experiments [1,7,8,9, 10] devoted to the study of the electronic properties of bulk h-BN, both the direct and the indirect band-gap are not yet accurately known, i.e., values ranging from 3.2 to 5.97 eV have been reported in the literature. In particular, the latest results were obtained by Watanabe et al [1], who showed that this material is very promising for ultraviolet laser devices and assumed, based on the strong luminescence peak observed at 5.765 eV, that it is a direct-band-gap semiconductor. In addition, they inferred a gap of 5.971 eV in contradiction with our results and other GW quasiparticle calculations [11,12,13].In this Letter, we use our all-electron GW approximation[14] to study for the first time the optical properties of bulk h-BN including electron-hole interaction effects and show that the previous experimental interpretation of the excitonic structure in the band gap is not correct. To perform this study we used state of the art methods, where both the self-energy effects and the solution of the Bethe-Salpeter equation [15] to compute the optical spectra from first principles [16]. In particular, our study confirms that this material is an indirectband-gap semicond...

A new implementation of the GW approximation (GWA) based on the all-electron ProjectorAugmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the plasmon-pole model. Two different ways of computing the self-energy are reported. The method is used successfully to determine the quasiparticle energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs, NaH and KH. To illustrate the novelty of the method the real and imaginary part of the frequency-dependent self-energy together with the spectral function of silicon are computed. Finally, the GWA results are compared with other calculations, highlighting that all-electron GWA results can differ markedly from those based on pseudopotential approaches.

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