Efficient GW calculations in two dimensional materials through a stochastic integration of the screened potential

Abstract

Many-body perturbation theory methods, such as the G0W0 approximation, are able to accurately predict quasiparticle (QP) properties of several classes of materials. However, the calculation of the QP band structure of two-dimensional (2D) semiconductors is known to require a very dense BZ sampling, due to the sharp q-dependence of the dielectric matrix in the long-wavelength limit (q → 0). In this work, we show how the convergence of the QP corrections of 2D semiconductors with respect to the BZ sampling can be drastically improved, by combining a Monte Carlo integration with an interpolation scheme able to represent the screened potential between the calculated grid points. The method has been validated by computing the band gap of three different prototype monolayer materials: a transition metal dichalcogenide (MoS2), a wide band gap insulator (hBN) and an anisotropic semiconductor (phosphorene). The proposed scheme shows that the convergence of the gap for these three materials up to 50meV is achieved by using k-point grids comparable to those needed by DFT calculations, while keeping the grid uniform.

Exciton-Driven and Layer-Independent Linear and Nonlinear Optical Properties in NbOCl2

“…28 For 2D systems, the random integration method and truncated Coulomb potential method are adopted to accelerate the convergence of bandgaps. 29 Moreover, a recently developed accelerating technique based on stochastic integration of the screened potential is used, 30 which allows the collection of GW-converged results using reduced Monkhorst−Pack k-point grids. The absorption spectra are obtained by the solution of the Bethe−Salpeter equation (BSE) 31 for which 10 (17) highest valence bands and 10 (17) lowest conduction bands for 2D (bulk) systems are set to describe the excitons.…”

Transitions in Xenes between excitonic, topological and trivial insulator phases: Influence of screening, band dispersion and external electric field

“…Instead, at the GW and BSE level the convergence of the Coulomb integral requires an explicit cutoff procedure which cuts the long-range part of the interaction by modifying the expression for the Coulomb operator in reciprocal space [63,64] . Calculations performed in this paper make usage of this technique, as implemented in the Yambo code, where also Monte Carlo integration method is introduced to deal with the long-wavelength limit of the 2D screening [65]. For an investigation of the influence of the cutoff procedures on optical properties and screening see also [66].…”