Evolution of local edge state braiding and spin topological transport characterization of Te-doped monolayer 1T'-MoS 2 .

We conducted first-principles calculations to investigate the dynamic braiding of local edge states and the spin topological transport mechanism in a strong topological MoS 1.75 Te 0.25 matrix. The presence of type-II Van Hove singularity in the middle of the X - S path indicates a strong cohesive interaction and a paring condensation mechanism within the matrix. The surface state data of MoS 1.75 Te 0.25 clearly demonstrate the characteristic features of strong regular loop braiding in spin transport. The spin Hall conductivity of the matrix was determined from the anisotropic characteristics of the spin Berry curvature. The phase transition of the spin Hall conductivity was evidenced by the positive sign of local spin polarization strength, primarily contributed by the d z 2 orbital of Mo atoms, and the negative sign of spin polarization strength, mainly contributed by the p-p x orbitals of S atoms. Moreover, the inclusion of Te selectively tuned the spin transport efficiency of the d z 2 and p x orbitals. Comprehensive braiding and readout of edge states can be achieved using an artificially designed MoS 1.75 Te 0.25 spintronic device. This 2D fractional braiding holds significant potential for applications in topological quantum computation.