Spin splitting with persistent spin textures induced by the line defect in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:math> phase of monolayer transition metal dichalcogenides

Abstract

The spin splitting driven by spin-orbit coupling in the monolayer (ML) transition metal dichalcogenide (TMDC) family has been widely studied only for the $1H$-phase structure, while its $1T$-phase structure has not been as widely researched due to the centrosymmetry of the crystal. Based on first-principles calculations, we show that significant spin splitting can be induced in the ML $1T$-TMDCs by introducing the line defect. Taking the ML ${\mathrm{PtSe}}_{2}$ as a representative example, we considered the stablest form of the line defects, namely, the Se vacancy line defect (Se-VLD). We find that large spin splitting is observed in the defect states of the Se-VLD, exhibiting a highly unidirectional spin configuration in the momentum space. This peculiar spin configuration may yield the so-called persistent spin textures (PSTs), a specific spin structure resulting in protection against spin decoherence and supporting an extraordinarily long spin lifetime. Moreover, by using $\stackrel{P\vec}{k}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{p}$ perturbation theory supplemented with symmetry analysis, we clarified that the emerging of the spin splitting maintaining the PSTs in the defect states originates from the inversion symmetry breaking together with the one-dimensional nature of the Se-VLD engineered ML ${\mathrm{PtSe}}_{2}$. Our findings pave a possible way to induce significant spin splitting in the ML $1T$-TMDCs, which could be highly important for designing spintronic devices.