First-principles calculations based on many-electron perturbation theory methods, such as the ab initio $GW$ and $GW$ plus Bethe-Salpeter equation ($GW$-BSE) approach, are reliable ways to predict quasiparticle and optical properties of materials, respectively. However, these methods involve more care in treating the electron-electron interaction and are considerably more computationally demanding when applied to systems with reduced dimensionality, since the electronic confinement leads to a slower convergence of sums over the Brillouin zone due to a much more complicated screening environment that manifests in the “head” and “neck” elements of the dielectric matrix. Here we present two schemes to sample the Brillouin zone for $GW$ and $GW$-BSE calculations: the nonuniform neck subsampling method and the clustered sampling interpolation method, which can respectively be used for a family of single-particle problems, such as $GW$ calculations, and for problems involving the scattering of two-particle states, such as when solving the BSE. We tested these methods on several few-layer semiconductors and graphene and show that they perform a much more efficient sampling of the Brillouin zone and yield two to three orders of magnitude reduction in the computer time. These two methods can be readily incorporated into several ab initio packages that compute electronic and optical properties through the $GW$ and $GW$-BSE approaches.

• Received 20 October 2016

DOI:https://doi.org/10.1103/PhysRevB.95.035109