Stochastic many-body perturbation theory for Moir\'e states in twisted bilayer phosphorene

TL;DR

This paper introduces a cost-effective stochastic many-body perturbation theory method for large twisted bilayer phosphorene systems, revealing how twisting influences electronic properties and impurity states.

Contribution

The paper presents a novel stochastic implementation of GW methods for large 2D systems, enabling the study of Moiré effects in twisted bilayer phosphorene with over 2,700 atoms.

Findings

Twisted bilayers show band splitting and localized impurity states.

Structural changes lift band degeneracies.

Impurity state energies depend on twisting angle.

Abstract

A new implementation of stochastic many-body perturbation theory for periodic 2D systems is presented. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. Excitation energies are studied using stochastic $G_0W_0$ and partially self-consistent $\bar \Delta GW_0$ 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 $\approx 3.1^\circ$. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moir\'e 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 Moir\'{e} superstructures.