First-principles calculations of the structural and electronic properties of monolayer $1T\text{−}{\mathrm{MoO}}_2$ and ${\mathrm{WO}}_2$

Two-dimensional transition metal dichalcogenides (TMDCs), such as ${\mathrm{MoS}}_2$ and ${\mathrm{WTe}}_2$, received extensive attention owing to their diverse crystal structures and intriguing physical properties. In contrast, there has been relatively limited research on transition-metal dioxides (TMDOs) despite sharing the same crystal structures with TMDCs. Here, we investigate the structural and electronic properties of monolayer $T$-phase ${\mathrm{MoO}}_2$ and ${\mathrm{WO}}_2$ using first-principles calculations. Our analysis reveals that their phonon dispersions have prominent imaginary modes, leading to the emergence of two charge density wave phases: $1{\text{T}}^{\prime }$ and $\sqrt{3}\times \sqrt{3}$. Interestingly, we find that $1{\text{T}}^{\prime }\text{−}{\mathrm{MoO}}_2$ and ${\mathrm{WO}}_2$ exhibit Dirac semimetal behavior, while their $\sqrt{3}\times \sqrt{3}$ phases are ferroelectric semiconductors, with out-of-plane spontaneous polarization of 3.99 and 3.94 pC/m, respectively. This work sheds light on structural and electronic properties of $T$-phase ${\mathrm{MoO}}_2$ and ${\mathrm{WO}}_2$, offering valuable insights for further experimental investigations into similar TMDOs materials.