Graphene-like Dirac states and quantum spin Hall insulators in square-octagonal MX2 (M= Mo, W; X= S, Se, Te) isomers

We studied the square-octagonal lattice of the transition metal dichalcogenide MX2 (with M=Mo, W; X=S, Se, and Te), as an isomer of the normal hexagonal compound of MX2. By band-structure calculations, we observe the graphene-like Dirac band structure in a rectangular lattice of MX2 with nonsymmorphic space group symmetry. Two bands with van Hove singularity points cross each at the Fermi energy, leading to two Dirac cones that locate at opposite momenta. Spin-orbit coupling can open a gap at these Dirac points, inside which gapless topological edge states exists as the quantum spin Hall (QSH) effect, the 2D topological insulator.