Polar and layered wide-bandgap semiconductors WO2Cl2 and MoO2Br2 with giant birefringence, large second harmonic and ferroelectric photovoltaic effects

van der Waals (vdW) layered semiconductors exhibiting large nonlinear-optical (NLO) effects have substantial potential for developing nanoscale quantum optical devices. ${\mathrm{NbOCl}}_{2}$, an ultrathin quantum light source, has recently displayed a large second harmonic effect. However, its small bandgap (\ensuremath{\sim}1.8 eV) impedes transparent light conversion across wide spectral regions, especially when utilizing practical 1-\textmu{}m lasers. In this paper, we found that ${M\mathrm{O}}_{2}{X}_{2}$ $(M=\mathrm{W}, \mathrm{Mo}; X=\mathrm{Cl}, \mathrm{Br})$ effectively widens the bandgap by using ${\mathrm{W}}^{6+}$ or $\mathrm{M}{\mathrm{o}}^{6+}$ instead of $\mathrm{N}{\mathrm{b}}^{4+}$ to eliminate in-gap nonbonding orbitals. Meanwhile, the octahedral $[{M\mathrm{O}}_{4}{X}_{2}]$ motifs display polar Jahn-Teller distortions as large as $[{\mathrm{NbO}}_{2}{X}_{4}]$ to demonstrate comparable NLO polarization effects. Based on first-principles calculations, ${\mathrm{WO}}_{2}{\mathrm{Cl}}_{2}$ and ${\mathrm{MoO}}_{2}{\mathrm{Br}}_{2}$ are predicted to possess wider bandgaps (2.9 and 2.2 eV), giant birefringence (0.5--0.7), and significant second harmonic and ferroelectric photovoltaic effects competitive with $\mathrm{NbO}{X}_{2}$. These findings provide strong incentives to explore new vdW materials with superior NLO properties.