Spontaneous breaking of time-reversal symmetry at the edges of 1T′ monolayer transition metal dichalcogenides

Using density functional theory (DFT) calculations and the Greens's function formalism, we report the existence of magnetic edge states with a noncollinear spin texture present on different edges of the $1{T}^{\ensuremath{'}}$ phase of the three monolayer transition metal dichalcogenides (TMDs): ${\mathrm{M}oS}₂, {\mathrm{M}oTe}₂$, and ${\mathrm{W}Te}₂$. The magnetic states are gapless and accompanied by a spontaneous breaking of the time-reversal symmetry. This may have an impact on the prospects of utilizing ${\mathrm{W}Te}₂$ as a quantum spin Hall insulator. It has previously been suggested that the topologically protected edge states of the $1{T}^{\ensuremath{'}}$ TMDs could be switched off by applying a perpendicular electric field [X. Qian, J. Liu, L. Fu, and J. Li, Science 346, 1344 (2014)]. We confirm with fully self-consistent DFT calculations that the topological edge states can be switched off. The investigated magnetic edge states are seen to be robust and remain gapless when applying a field.