  The influence of an external electric field on single-layer transition-metal
dichalcogenides TX2 with T = Mo, W and X = S, Se (MoWSeS) have been
investigated by means of density-functional theory within two-dimensional
periodic boundary conditions under consideration of relativistic effects
including the spin-orbit interactions. Our results show that the external field
modifies the band structure of the monolayers, in particular the conduction
band. This modification has, however, very little influence on the band gap and
effective masses of holes and electrons at the K point, and also the spin-orbit
splitting of these monolayers is almost unaffected. Our results indicate a
remarkable stability of the electronic properties of TX2 monolayers with
respect to gate voltages. A reduction of the electronic band gap is observed
only starting from field strengths of 2.0 V per {\AA} (3.5 V per {\AA}) for
selenides (sulphides), and the transition to a metallic phase would occur at
fields of 4.5 V per {\AA} (6.5 V per {\AA}).
