  The metal-insulator transition (MIT) driven by electronic correlations is a
fundamental and challenging problem in condensed-matter physics. Particularly,
whether such a transition can be continuous remains open. The emergence of
semiconducting moir\'e materials with continuously tunable bandwidth provides
an ideal platform to study interaction-driven MITs. Although a bandwidth-tuned
MIT at fixed full electron filling of the moir\'e superlattice has been
reported recently, that at fractional filling, which involves translational
symmetry breaking of the underlying superlattice, remains elusive. Here, we
demonstrate bandwidth-tuned MITs in a MoSe2/WS2 moir\'e superlattice at both
integer and fractional fillings using the exciton sensing technique. The
bandwidth is controlled by an out-of-plane electric field. The dielectric
response is probed optically with the 2s exciton in a remote WSe2 sensor layer.
The exciton spectral weight is negligible for the metallic state, consistent
with a large negative dielectric constant. It continuously vanishes when the
transition is approached from the insulating side, corresponding to a diverging
dielectric constant or a "dielectric catastrophe". Our results support
continuous interaction-driven MITs in a two-dimensional triangular lattice and
stimulate future explorations of exotic quantum phases, such as quantum spin
liquids, in their vicinities.
