  We use electron transport to characterize monolayer graphene - multilayer
MoS2 heterostructures. Our samples show ambipolar characteristics and
conductivity saturation on the electron branch which signals the onset of MoS2
conduction band population. Surprisingly, the carrier density in graphene
decreases with gate bias once MoS2 is populated, demonstrating negative
compressibility in MoS2. We are able to interpret our measurements
quantitatively by accounting for disorder and using the random phase
approximation (RPA) for the exchange and correlation energies of both Dirac and
parabolic-band two-dimensional electron gases. This interpretation allows us to
extract the energetic offset between the conduction band edge of MoS2 and the
Dirac point of graphene.
