Combined subsampling and analytical integration for efficient large-scale G W calculations for 2D systems

Accurate and efficient predictions of the quasiparticle properties of complex materials remain a major challenge due to the convergence issue and the unfavorable scaling of the computational cost with respect to the system size. Quasiparticle GW calculations for two-dimensional (2D) materials are especially difficult. The unusual analytical behaviors of the dielectric screening and the electron self-energy of 2D materials make the conventional Brillouin zone (BZ) integration approach rather inefficient and require an extremely dense k-grid to properly converge the calculated quasiparticle energies. In this work, we present a combined nonuniform subsampling and analytical integration method that can drastically improve the efficiency of the BZ integration in 2D GW calculations. Our work is distinguished from previous work in that, instead of focusing on the intricate dielectric matrix or the screened Coulomb interaction matrix, we exploit the analytical behavior of various terms of the convolved self-energy Σ(q) in the small q limit. This method, when combined with another accelerated GW method that we developed recently, can drastically speed up (by over three orders of magnitude) GW calculations for 2D materials. Our method allows fully converged GW calculations for complex 2D systems at a fraction of computational cost, facilitating future high throughput screening of the quasiparticle properties of 2D semiconductors for various applications. To demonstrate the capability and performance of our new method, we have carried out fully converged GW calculations for monolayer C₂N, a recently discovered 2D material with a large unit cell, and investigate its quasiparticle band structure in detail.