Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations

The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For gaps, semilocal density functionals up to the generalized gradient (GGA) level cannot compete with accuracy of hybrid-based approximations or GW. Meta-GGA strong dependence on kinetic energy ingredient potentially give wider gaps compared GGAs. recent TASK meta-GGA functional from Aschebrock and K\"ummel [Phys. Rev. Research 1, 033082 (2019)], is constructed an enhanced nonlocality in Kohn-Sham scheme therefore harbors great opportunities for gap prediction. Although this was found yield excellent bulk solids, straightforwardly transferred low-dimensional materials. reduced screening these materials results larger their counterparts, as additional barrier overcome. In paper we demonstrate how alteration affects monolayers nanoribbons present accurate competing revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. order achieve goal, have modified (a) changing tight upper bound one- two-electron systems (${h}_{X}^{0}$) 1.174 1.29 (b) limit interpolation function ${f}_{X}(\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$) that interpolates exchange enhancement factor ${F}_{X}(s,\ensuremath{\alpha})$ $\ensuremath{\alpha}=0$ 1. resulting (mTASK) tested various three dimensions two one dimension (nanoribbons) higher-level hybrid HSE06 ${\mathrm{G}}_{0}{\mathrm{W}}_{0}$ within many-body perturbation theory. We find mTASK systematically improves structures two-dimensional (2D) 1D systems, without significantly affecting original 3D materials, when Perdew-Burke-Ernzerhof (PBE) GGA strongly constrained appropriately normed (SCAN) meta-GGA. further applicability assessing transition metal dichalcogenide respect bending curvatures.