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Stability of metallic edges and Fermi-level pinning in transition-metal dichalcogenide nanoribbons

Nanoribbons of MoS$_2$ present a unique electronic structure that consists of a semiconducting bulk bounded by metallic edges; same holds for other Transition-Metal Dichalcogenides (TMDs) (Mo-,W-,S$_{2}$,Se$_{2}$). We perform first-principles calculations for TMD nanoribbons with reconstructed zig-zag metal terminated edges that contain chalcogen adatoms. All nanorobbons have possitive edge energies when the chemical potential of chalcogens is close to the energy of solids, and negative edge energies for high chemical potential. The reconstruction with two chalcogen adatoms is expected to be the most stable one. In all nanoribbons, a metallic phase is found near their edges, with the Fermi level of this metallic phase being lower than the Fermi level of the 2D material.