Electric Field Effects on Armchair MoS2 Nanoribbons

{\it Ab initio} density functional theory calculations are performed to investigate the electronic structure of MoS$_2$ armchair nanoribbons in the presence of an external static electric field. Such nanoribbons, which are nonmagnetic and semiconducting, exhibit a set of weakly interacting edge states whose energy position determines the band-gap of the system. We show that, by applying an external transverse electric field, $E_\mathrm{ext}$, the nanoribbons band-gap can be significantly reduced, leading to a metal-insulator transition beyond a certain critical value. Moreover, the presence of a sufficiently high density of states at the Fermi level in the vicinity of the metal-insulator transition leads to the onset of Stoner ferromagnetism that can be modulated, and even extinguished, by $E_\mathrm{ext}$. In the case of bi-layer nanoribbons we further show that the band-gap can be changed from indirect to direct by applying a transverse field, an effect which might be of significance for opto-electronics applications.