Efficient many-body calculations for two-dimensional materials using exact limits for the screened potential: Band gaps of MoS2, h-BN, and phosphorene

Calculating the quasiparticle (QP) band structure of two-dimensional (2D) materials within the GW self-energy approximation has proven to be a rather demanding computational task. The main reason is the strong q dependence of the 2D dielectric function around q = 0 that calls for a much denser sampling of the Brillouin zone (BZ) than is necessary for similar three-dimensional solids. Here, we use an analytical expression for the small q limit of the 2D response function to perform the BZ integral over the critical region around q = 0. This drastically reduces the requirements on the q-point mesh and implies a significant computational speedup. For example, in the case of monolayer MoS2, convergence of the G(0)W(0) band gap to within similar to 0.1 eV is achieved with 12 x 12 q points rather than the 36 x 36 mesh required with discrete BZ sampling techniques. We perform a critical assessment of the band gap of the three prototypical 2D semiconductors, MoS2, h-BN, and phosphorene, including the effect of self-consistency at the GW(0) level. The method is implemented in the open source code GPAW.