Universal polarization energies for defects in monolayer, surface and bulk hexagonal boron nitride : A finite-size fragments GW approach

TL;DR

This paper introduces a finite-size fragment GW approach to accurately study defect energy levels in hexagonal boron nitride across monolayer, surface, and bulk forms, revealing universal polarization energy behaviors.

Contribution

The paper presents a novel fragment GW method that simplifies the study of defect energies in layered materials by capturing dielectric effects with finite-size fragments.

Findings

Defect energy levels evolve predictably with layer number due to screening.

Polarization energies follow a simple inverse relation with layer count, with near-universal coefficients.

Results enable extrapolation from monolayer to multilayer and bulk h-BN defect levels.

Abstract

We study defect energy levels in hexagonal boron-nitride with varying number of layers using a fragment many-body $GW$ formalism, taking as examples the paradigmatic carbon-dimer and $C_BV_N$ defects. We show that a single layer can be fragmented in polarizable finite-size areas reproducing faithfully the effect of the dielectric environment, dramatically facilitating the study at the many-body level of point defects in the dilute limit. The evolution of defect energy levels from the monolayer to a $n$-layer system due to increased screening, labeled polarization energies, follow a simple $({\Delta P}/n + P_{\infty})$ behavior. The coefficients $\Delta P$ and $P_{\infty}$ are found to be close-to-universal, with opposite signs for holes and electrons, characterizing mainly the host and the position of the defect (surface or bulk), but hardly the defect type. Our results rationalize the evolution of defect energy levels with layers number, allowing to safely extrapolate results obtained for the monolayer to few-layers, surface or bulk \textit{h}-BN. The present many-body fragment approach further opens the door to studying disordered 2D layers.