  Van der Waals heterostuctures, made from stacks of two-dimensional materials,
exhibit unique light-matter interactions and are promising for novel
optoelectronic devices. The performance of such devices is governed by
near-field coupling through, e.g., interlayer charge and/or energy transfer.
New concepts and experimental methodologies are needed to properly describe
two-dimensional heterointerfaces. Here, we report on interlayer charge and
energy transfer in atomically thin metal (graphene)/semiconductor (transition
metal dichalcogenide (TMD, here MoSe$_2$)) heterostructures using a combination
of photoluminescence and Raman scattering spectroscopies. The photoluminescence
intensity in graphene/MoSe$_2$ is quenched by more than two orders of magnitude
and rises linearly with the photon flux, demonstrating a drastically shortened
($\sim 1~\tr{ps}$) room temperature MoSe$_2$ exciton lifetime. Key
complementary insights are provided from analysis of the graphene and MoSe$_2$
Raman modes, which reveals net photoinduced electron transfer from MoSe$_2$ to
graphene and hole accumulation in MoSe$_2$. Remarkably, the steady state Fermi
energy of graphene saturates at $290\pm 15~\tr{meV}$ above the Dirac point.
This behavior is observed both in ambient air and in vacuum and is discussed in
terms of band offsets and environmental effects. In this saturation regime,
balanced photoinduced flows of electrons and holes may transfer to graphene, a
mechanism that effectively leads to energy transfer. Using a broad range of
photon fluxes and diverse environmental conditions, we find that the presence
of net photoinduced charge transfer has no measurable impact on the near-unity
photoluminescence quenching efficiency in graphene/MoSe$_2$. This absence of
correlation strongly suggests that energy transfer to graphene is the dominant
interlayer coupling mechanism between atomically-thin TMDs and graphene.
