  Two-dimensional (2D) semiconductors, such as the transition metal
dichalcogenides, have demonstrated tremendous promise for the development of
highly tunable quantum devices. Realizing this potential requires
low-resistance electrical contacts that perform well at low temperatures and
low densities where quantum properties are relevant. Here we present a new
device architecture for 2D semiconductors that utilizes a charge-transfer layer
to achieve large hole doping in the contact region, and implement this
technique to measure magneto-transport properties of high-purity monolayer
WSe$_2$. We measure a record-high hole mobility of 80,000 cm$^2$/Vs and access
channel carrier densities as low as $1.6\times10^{11}$ cm$^{-2}$, an order of
magnitude lower than previously achievable. Our ability to realize transparent
contact to high-mobility devices at low density enables transport measurement
of correlation-driven quantum phases including observation of a low temperature
metal-insulator transition in a density and temperature regime where Wigner
crystal formation is expected, and observation of the fractional quantum Hall
effect under large magnetic fields. The charge transfer contact scheme paves
the way for discovery and manipulation of new quantum phenomena in 2D
semiconductors and their heterostructures.
