Strong unidirectional Rashba state induced by extended vacancy line defects in a $1T'$-WTe$_{2}$ monolayer

The correlation between spin-orbit coupling and low crystal symmetry in the $1T'$ phase of the tungsten ditellurides (WTe$_{2}$) monolayer (ML) plays a significant role in its electronic and topological properties. However, the centrosymmetric nature of the crystal maintains Kramer's spin degeneracy in its electronic states, which limits its functionality in spintronics. In this paper, through a systematic study using first-principles calculations, we show that significant spin splitting can be induced in the $1T'$-WTe$_{2}$ ML by introducing one dimensional (1D) vacancy line defect (VLD). We examine six configurations of the 1D VLD, which consist of three VLDs extended in the armchair direction including a Te$_{1}$ armchair-VLD ($ACV_{\texttt{Te}_{1}}$), Te$_{2}$ armchair-VLD ($ACV_{\texttt{Te}_{2}}$), and W armchair-VLD ($ACV_{\texttt{W}}$); and three VLDs elongated along the zigzag direction comprising a Te$_{1}$ zigzag-VLD ($ZZV_{\texttt{Te}_{1}}$), Te$_{2}$ zigzag-VLD ($ZZV_{\texttt{Te}_{2}}$), and W zigzag-VLD ($ZZV_{\texttt{W}}$), where Te$_{1}$ and Te$_{2}$ are two nonequivalent Te atoms located at the lower and higher sites in the top layer, respectively. We find that both the $ACV_{\texttt{Te}_{1}}$ and $ACV_{\texttt{W}}$ systems have the lowest formation energy. Concerning these two most stable VLD systems, we identify large spin splitting in the defect states near the Fermi level driven by a strong coupling of the in-plane $p-d$ orbitals, displaying highly unidirectional Rashba states with perfectly collinear spin configurations in the momentum space. This unique spin configuration gives rise to a specific spin mode that protects the spin from decoherence and leads to an exceptionally long spin lifetime...........