First-principles calculations of the structural and electronic properties of monolayer 1T−MoO2 and WO2

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: $1{\mathit{\text{T}}}^{\ensuremath{'}}$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$. Interestingly, we find that $1{\mathit{\text{T}}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{MoO}}_{2}$ and ${\mathrm{WO}}_{2}$ exhibit Dirac semimetal behavior, while their $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ 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.