  In few-layer (FL) transition metal dichalcogenides (TMDC), the conduction
bands along the Gamma-K directions shift downward energetically in the presence
of interlayer interactions, forming six Q valleys related by three-fold
rotational symmetry and time reversal symmetry. In even-layers the extra
inversion symmetry requires all states to be Kramers degenerate, whereas in
odd-layers the intrinsic inversion asymmetry dictates the Q valleys to be
spin-valley coupled. In this Letter, we report the transport characterization
of prominent Shubnikov-de Hass (SdH) oscillations for the Q valley electrons in
FL transition metal disulfide (TMDs), as well as the first quantum Hall effect
(QHE) in TMDCs. Our devices exhibit ultrahigh field-effect mobilities (~16,000
cm2V-1s-1 for FL WS2 and ~10,500 cm2V-1s-1 for FL MoS2) at cryogenic
temperatures. Universally in the SdH oscillations, we observe a valley Zeeman
effect in all odd-layer TMD devices and a spin Zeeman effect in all even-layer
TMD devices.
