Efficient GW calculations in two dimensional through the interpolation of the screened potential

The GW self-energy approximation is able to accurately predict quasiparticle (QP) properties of several classes of materials. However, the calculation of the QP band structure of 2D semiconductors is challenging due to the sharp q-dependence of the dielectric function in the long-wavelength limit (q→0). In this case, a very dense q-sampling of the Brillouin zone is usually needed to obtain properly converged quantities. In this work, we assess the possibility to drastically improve the convergence of the QP corrections of 2D semiconductors with respect to the q-sampling, by combining Monte Carlo integration techniques and interpolation schemes of the screened potential. We test our method by computing the bandgap for three prototypical materials: a wide bandgap insulator (hBN), a transition metal dichalcogenide (MoS₂), and an anisotropic semiconductor (phosphorene). A speed-up of at least two orders of magnitude is found for all the systems considered.