We report that an external electric field applied normal to bilayers of transition-metal dichalcogenides ${TX}_2$ ($T = \mathrm{Mo}$, W, $X = \mathrm{S}$, Se) creates significant spin-orbit splittings and reduces the electronic band gap linearly with the field strength. Contrary to the ${TX}_2$ monolayers, spin-orbit splittings and valley polarization are absent in bilayers due to the presence of inversion symmetry. This symmetry can be broken by an electric field, and the spin-orbit splittings in the valence band quickly reach values similar to those in the monolayers (145 meV for ${\mathrm{MoS}}_2,...,$ 418 meV for ${\mathrm{WSe}}_2$) at saturation fields less than $500 \mathrm{mV} {\AA }^{-1}$. The band gap closure results in a semiconductor-metal transition at field strength between 1.25 ($\mathrm{W}{X}_2$) and 1.50 (${\text{Mo}X}_2$) $\mathrm{V} {\AA }^{-1}$. Thus, by using a gate voltage, the spin polarization can be switched on and off in ${TX}_2$ bilayers, thus activating them for spintronic and valleytronic applications.

• Received 16 April 2014
• Revised 17 June 2014

DOI:https://doi.org/10.1103/PhysRevB.90.125440