Polar and layered wide-bandgap semiconductors ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$ 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 (∼1.8 eV) impedes transparent light conversion across wide spectral regions, especially when utilizing practical 1-µm 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 $\left[{M\mathrm{O}}_4{X}_2\right]$ motifs display polar Jahn-Teller distortions as large as $\left[{\mathrm{NbO}}_2{X}_4\right]$ 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.

Figure 1

Strategy for optimizing ${\mathrm{NbOCl}}_2$. Schematic diagram of band structure modulation of ${\mathrm{NbOCl}}_2$ vs ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ (a), and Jahn-Teller distortion optimization of $\left[{\mathrm{NbO}}_2{\mathrm{Cl}}_4\right]$ vs $\left[{\mathrm{WO}}_4{\mathrm{Cl}}_2\right]$ (b).

Figure 2

Crystal and electronic structures of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$. (a) Monolayer structure of ${M\mathrm{O}}_2{X}_2$. By AA and AB stacking, ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ (b) and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$ (c) crystals are crystallized in $Pmc{2}_1$ and Cc space groups, respectively. Orbital-projected band structures and PDOS of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ (d) and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$ (e) indicate no nonbonding orbitals at the top of VB.

Figure 3

Comparison on distortion, polarity, and anisotropy of ${M\mathrm{O}}_2{X}_2$ vs $\mathrm{NbO}{X}_2$. (a) Bandgap $E_g$, Lalik distortion index ΔH (b), electronic dipole moment $q_{\mathrm{etot}}$ (c), and birefringence $\mathrm{\Delta }n$ (d) of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$, ${\mathrm{MoO}}_2{\mathrm{Br}}_2$, ${\mathrm{NbOCl}}_2$ and ${\mathrm{NbOBr}}_2$.

Figure 4

NLO characterization and mechanism of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$. Angle-dependent SHG responses of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$ at polarization angles of 0° (a), 30° (b), and 60° (c) as compared to ${\mathrm{NbOCl}}_2$ and ${\mathrm{NbOBr}}_2$. The maximum value of $I_{\mathrm{SHG}}$ with respect to the polarization angle θ (d), the real part of dynamical SHG responses (e), and shift current susceptibilities (f) of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$ vs ${\mathrm{NbOCl}}_2$ and ${\mathrm{NbOBr}}_2$. Shift current ${\sigma }_{xxx}$ spectra (g), the imaginary part of dielectric function ${\varepsilon }_2^{xx}$ (h), and shift vector (i) of ${\mathrm{WO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{MoO}}_2{\mathrm{Br}}_2$. The highlighted region marks the range of peaks.