  Charge transport in MoS2 in the low carrier density regime is dominated by
trap states and band edge disorder. The intrinsic transport properties of MoS2
emerge in the high density regime where conduction occurs via extended states.
Here, we investigate the transport properties of mechanically exfoliated mono-,
bi-, and trilayer MoS2 sheets over a wide range of carrier densities realized
by a combination of ion gel top gate and SiO2 back gate which allows us to
achieve high charge carrier (>10^13) density. We discuss the gating properties
of the devices as a function of layer thickness and demonstrate resistivities
of as low as 1 k{\Omega} for monolayer and 420{\Omega} for bilayer devices at
10 K. We show that from the capacitive coupling of the two gates, quantum
capacitance can be roughly estimated to be on the order of 1 {\mu}F/cm^2 for
all devices studied. Temperature dependence of the carrier mobility in the high
density regime indicates that short-range scatterers limit charge transport at
low temperatures.
