  The recent TASK meta-GGA density functional [Phys. Rev. Research, 1, 033082
(2019)] is constructed with an enhanced nonlocality in the generalized
Kohn-Sham scheme, and therefore harbors great opportunities for band gap
prediction. Although this approximation was found to yield excellent band gaps
of bulk solids, this accuracy cannot be straightforwardly transferred to
low-dimensional materials. The reduced screening of these materials results in
larger band gaps compared to their bulk counterparts, as an additional barrier
to overcome. In this work, we demonstrate how the alteration of exact physical
constraints in this functional affects the band gaps of monolayers and
nanoribbons, and present accurate band gaps competing with the HSE06
approximation. In order to achieve this goal, we have modified the TASK
functional (a) by changing the tight upper-bound for one or two-electron
systems ($h_X^0$) from 1.174 to 1.29 (b) by changing the limit of interpolation
function $f_X (\alpha \rightarrow \infty$) of the TASK functional that
interpolates the exchange enhancement factor $F_X (s,\alpha)$ from $\alpha=$ 0
to 1. The resulting modified TASK (mTASK) was tested for various materials from
3D to 2D to 1D (nanoribbons), and was compared with the results of the
higher-level hybrid functional HSE06 or with the G$_0$W$_0$ approximation
within many-body perturbation theory. We find that mTASK greatly improves the
band gaps and band structures of 2D and 1D systems, without significantly
affecting the accuracy of the original TASK for the bulk 3D materials, when
compared to the PBE-GGA and SCAN meta-GGA. We further demonstrate the
applicability of mTASK by assessing the band structures of TMD nanoribbons with
respect to various bending curvatures.
