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We present our study on atomic, electronic, magnetic and phonon properties ofone dimensional honeycomb structure of molybdenum disulfide (MoS$_2$) usingfirst-principles plane wave method. Calculated phonon frequencies of barearmchair nanoribbon reveal the fourth acoustic branch and indicate thestability. Force constant and in-plane stiffness calculated in the harmonicelastic deformation range signify that the MoS$_2$ nanoribbons are stiff quasione dimensional structures, but not as strong as graphene and BN nanoribbons.Bare MoS$_2$ armchair nanoribbons are nonmagnetic, direct band gapsemiconductors. Bare zigzag MoS$_2$ nanoribbons become half-metallic as aresult of the (2x1) reconstruction of edge atoms and are semiconductor forminority spins, but metallic for the majority spins. Their magnetic moments andspin-polarizations at the Fermi level are reduced as a result of thepassivation of edge atoms by hydrogen. The functionalization of MoS$_2$nanoribbons by adatom adsorption and vacancy defect creation are also studied.The nonmagnetic armchair nanoribbons attain net magnetic moment depending onwhere the foreign atoms are adsorbed and what kind of vacancy defect iscreated. The magnetization of zigzag nanoribbons due to the edge states issuppressed in the presence of vacancy defects.

Mechanical and Electronic Properties of MoS$_2$ Nanoribbons and Their Defects