  We investigate how field-effect doping affects the structural properties, the
electronic structure and the Hall coefficient of few-layers transition metal
dichalcogenides by using density-functional theory. We consider mono-, bi-, and
trilayers of the H polytype of MoS2, MoSe2, MoTe2, WS2, and WSe2 and provide a
full database of electronic structures and Hall coefficients for hole and
electron doping. We find that, for both electron and hole doping, the
electronic structure depends on the number of layers and cannot be described by
a rigid band shift. Furthermore, it is important to relax the structure under
the asymmetric electric field. Interestingly, while the width of the conducting
channel depends on the doping, the number of occupied bands at each given k
point is almost uncorrelated with the thickness of the doping-charge
distribution. Finally, we calculate within the constant-relaxation-time
approximation the electrical conductivity and the inverse Hall coefficient. We
demonstrate that in some cases the charge determined by Hall-effect
measurements can deviate from the real charge by up to 50%. For hole-doped
MoTe2 the Hall charge has even the wrong polarity at low temperature. We
provide the mapping between the doping charge and the Hall coefficient. In the
appendix we present more than 250 band structures for all doping levels of the
transition-metal dichalcogenides considered within this work.
