  We highlight the emergence of metallic states in two-dimensional
transition-metal-dichalcogenide nanostructures -nanoribbons, islands, and
inversion domain boundaries- as a widespread and universal phenomenon driven by
the polar discontinuities occurring at their edges or boundaries. We show that
such metallic states form one-dimensional wires of electrons or holes, with a
free charge density that increases with the system size, up to complete
screening of the polarization charge, and can also be controlled by the
specific edge or boundary configurations, e.g. through chemisorption of
hydrogen or sulfur atoms at the edges. For triangular islands, local polar
discontinuities occur even in the absence of a total dipole moment for the
island and lead to an accumulation of free carriers close to the edges,
providing a consistent explanation of previous experimental observations. To
further stress the universal character of these mechanisms, we show that polar
discontinuities give rise to metallic states also at inversion domain
boundaries. These findings underscore the potential of engineering
transition-metal-dichalcogenide nanostructures for manifold applications in
nano- and opto-electronics, spintronics, catalysis, and solar-energy
harvesting.
