Charge/spin density waves at the edges and mirror twin boundaries of Transition Metal Di-Chalcogenides

Grain boundaries and edges of two-dimensional semiconducting TMDCs MX₂ (M=Mo,W; X=S,Se,Te) exhibit metallicity, which is remarkably robust against variations in structure or stoichiometry. The origin of these metallic boundary states lies in the lattice polarization and the states are topologically protected by the D_3h symmetry of the TMDC lattice. From first-principles (DFT+U) calculations we show, however, that symmetry breaking at edges or boundaries leads to one-dimensional charge and spin density wave (C/SDW) instabilities. Such C/SDWs are commensurable with a period of three lattice sites, dictated by the lattice symmetry, and open up a band gap. The resulting electronic structure agrees well with experimental measurements on, for instance, the mirror twin boundary.