Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals

Abstract

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [ 32097004 J. Chem. Theory Comput. 2020 16 2654 ] and GLLB-SC [ 115106 Phys. Rev. B 2010 82 ] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [ 033082 Phys. Rev. Res. 2019 1 ] and MGGAC [ 155140 Phys. Rev. B 2019 100 ], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [ 226401 19658882 Phys. Rev. Lett. 2009 102 ] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.

Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals

“…GLLB-SC band gaps have been calculated for 2D materials in the computational 2D materials database (C2DB) database [32,35,59], and it was shown that the agreement with the G 0 W 0 (one-shot GW [60]) band gaps is excellent [35]. A similar conclusion was drawn in our recent work where selected 2D systems were considered [42].…”

“…In one of our previous works on 2D materials [42], plots of the xc potentials were shown to provide an explanation to some of the observed trends. For instance, for XS 2 , XSe 2 , and XTe 2 , the PBE and LMBJ(β = 0.5) band gaps are basically the same when X = Mo or W, while it is not at all the case when X = Zr or Hf.…”

“…Such works on 2D systems related to the assessment of xc functionals for band gaps can be found in Refs. [18,[31][32][33][34][35][36][37][38][39][40][41][42]. We note that an important difference between bulk solids and 2D systems concerns the magnitude of the excitonic effect (present in optical measurements), which is an effect beyond the Kohn-Sham (KS) and GW methods.…”

“…In Refs. [35,38,39,42] for instance, GW band gaps were used for the testing of various xc DFT functionals on 2D materials (see Ref. [44] for bulk solids).…”

“…The goal of the present work is to provide a thorough assessment of DFT approximations for the band gap of 2D materials. It is a follow-up study of our recent works [39,42] devoted to a more systematic comparison of xc functionals. In particular some of the most recent MGGA functionals will be considered.…”