Nonunique fraction of Fock exchange for defects in two-dimensional materials
Wei Chen, Sinéad M. Griffin, Gian‐Marco Rignanese, Geoffroy Hautier
Abstract
By investigating the vacancy and substitutional defects in monolayer ${\mathrm{WS}}_{2}$ 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 on the band gap can lead to qualitatively incorrect defect physics in two-dimensional materials. Instead, excellent agreement is achieved with both experiment and many-body perturbation theory within the $GW$ approximation once the mixing parameters are tuned individually for the defect species 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 while the localized defects are subject to bulklike screening.