Nonunique fraction of Fock exchange for defects in two-dimensional materials

TL;DR

This paper demonstrates that in two-dimensional materials, the optimal Fock exchange fraction varies for defects and band edges, challenging the idea of a universal value, and emphasizes the importance of defect-specific tuning for accurate predictions.

Contribution

It reveals the nonuniqueness of Fock exchange fraction in 2D materials and proposes defect-specific tuning to improve accuracy in defect physics modeling.

Findings

No single Fock exchange value satisfies all conditions in 2D defects.

Tuning Fock exchange individually for defects and band edges yields better agreement with experiments.

Reduced screening in 2D systems causes inherent departure from a universal Fock exchange parameter.

Abstract

By investigating the vacancy and substitutional defects in monolayer WS$_2$ with hybrid functionals, we find that there is no unique amount of Fock exchange that concurrently satisfies the generalized Koopmans' condition and reproduces the band gap and band-edge positions. Fixing the mixing parameter of Fock exchange based upon the band gap can lead to qualitatively incorrect defect physics in two-dimensional materials. Instead, excellent agreement is achieved with experiment and many-body perturbation theory within $GW$ approximation once the mixing parameters are tuned individually for the defects and the band edges. We show the departure from a unique optimized mixing parameter is inherent to two-dimensional systems as the band edges experience a reduced screening whilst the localized defects are subject to bulklike screening.