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Graphene-like Dirac states and Quantum Spin Hall Insulators in the square-octagonal MX2 (M=Mo, W; X=S, Se, Te) Isomers

We studied the square-octagonal lattice of the transition metal dichalcogenide MX$_2$ (with $M$=Mo, W; $X$=S, Se and Te), as an isomer of the normal hexagonal compound of MX$_2$. By band structure calculations, we observe the graphene-like Dirac band structure in a rectangular lattice of MX$_2$ with nonsymmorphic space group symmetry. Two bands with van Hove singularity points cross each at the Fermi energy, leading to two Dirac cones that locates at opposite momenta. Spin-orbit coupling can open a nontrivial gap at these Dirac points and induce the quantum spin Hall (QSH) phase, the 2D topological insulator. Here, square-octagonal MX$_2$ structures realize the interesting graphene physics, such as Dirac bands and QSH effect, in the transition metal dichalcogenides.