Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene

We implement stochastic many-body perturbation theory for systems with 2D periodic boundary conditions. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. Excitation energies are studied using stochastic G0W0 and partially self-consistent ∆GW0 approaches. The approach is inexpensive; it is used to study twisted systems with unit cells containing > 2,700 atoms (> 13,500 valence electrons), which corresponds to a minimum twisting angle of ≈ 3.1◦. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moire impurity states, as documented by band-structure unfolding. Structural changes in twisted structures lift band degeneracies. Energies of the impurity states vary with the twisting angle due to an interplay between non-local exchange and polarization effects. The mechanisms of quasiparticle energy (de)stabilization due to twisting are likely applicable to a wide range of low-dimensional Moire superstructures.