  We have performed a comprehensive first-principles study of the electronic
and magnetic properties of two-dimensional (2D) transition-metal dichalcogenide
(TMD) heterobilayers MX2/MoS2 (M = Mo, Cr, W, Fe, V; X = S, Se). For M = Mo,
Cr, W; X=S, Se, all heterobilayers show semiconducting characteristics with an
indirect bandgap with the exception of the WSe2/MoS2 heterobilayer which
retains the direct-band-gap character of the constituent monolayer. For M = Fe,
V; X = S, Se, the MX2/MoS2 heterobilayers exhibit metallic characters.
Particular attention of this study has been focused on engineering bandgap of
the TMD heterobilayer materials via application of either a tensile strain or
an external electric field. We find that with increasing either the biaxial or
uniaxial tensile strain, the MX2/MoS2 (M=Mo, Cr, W; X=S, Se) heterobilayers can
undergo a semiconductor-to-metal transition. For the WSe2/MoS2 heterobilayer, a
direct-to-indirect bandgap transition may occur beyond a critical biaxial or
uniaxial strain. For M (=Fe, V) and X (=S, Se), the magnetic moments of both
metal and chalcogen atoms are enhanced when the MX2/MoS2 heterobilayers are
under a biaxial tensile strain. Moreover, the bandgap of MX2/MoS2 (M=Mo, Cr, W;
X=S, Se) heterobilayers can be reduced by the electric field. For two
heterobilayers MSe2/MoS2 (M=Mo, Cr), PBE calculations suggest that the
indirect-to-direct bandgap transition may occur under an external electric
field. The transition is attributed to the enhanced spontaneous polarization.
The tunable bandgaps in general and possible indirect-direct bandgap
transitions due to tensile strain or external electric field endow the TMD
heterobilayer materials a viable candidate for optoelectronic applications.
