  In Bernal stacked bilayer graphene interlayer coupling significantly affects
the electronic bandstructure compared to monolayer graphene. Here we present
magnetotransport experiments on high-quality $n$-doped bilayer MoS$_{2}$. By
measuring the evolution of the Landau levels as a function of electron density
and applied magnetic field we are able to investigate the occupation of
conduction band states, the interlayer coupling in pristine bilayer MoS$_{2}$,
and how these effects are governed by electron-electron interactions. We find
that the two layers of the bilayer MoS$_{2}$ behave as two independent
electronic systems where a two-fold Landau level's degeneracy is observed for
each MoS$_{2}$ layer. At the onset of the population of the bottom MoS$_{2}$
layer we observe a large negative compressibility caused by the exchange
interaction. These observations, enabled by the high electronic quality of our
samples, demonstrate weak interlayer tunnel coupling but strong interlayer
electrostatic coupling in pristine bilayer MoS$_{2}$. The conclusions from the
experiments may be relevant also to other transition metal dichalcogenide
materials.

Mesoscale and Nanoscale Physics