  The ability to directly observe electronic band structure in modern nanoscale
field-effect devices could transform understanding of their physics and
function. One could, for example, visualize local changes in the electrical and
chemical potentials as a gate voltage is applied. One could also study
intriguing physical phenomena such as electrically induced topological
transitions and many-body spectral reconstructions. Here we show that submicron
angle-resolved photoemission (micro-ARPES) applied to two-dimensional (2D) van
der Waals heterostructures affords this ability. In graphene devices, we
observe a shift of the chemical potential by 0.6 eV across the Dirac point as a
gate voltage is applied. In several 2D semiconductors we see the conduction
band edge appear as electrons accumulate, establishing its energy and momentum,
and observe significant band-gap renormalization at low densities. We also show
that micro-ARPES and optical spectroscopy can be applied to a single device,
allowing rigorous study of the relationship between gate-controlled electronic
and excitonic properties.
