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

Chen, Wei [UCL] Griffin, Sinéad M. [Molecular Foundry Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA] Rignanese, Gian-Marco [UCL] Hautier, Geoffroy [UCL]

By investigating the vacancy and substitutional defects in monolayer WS2 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.