  Emergent quantum phases driven by electronic interactions can manifest in
materials with narrowly dispersing, i.e. "flat", energy bands. Recently, flat
bands have been realized in a variety of graphene-based heterostructures using
the tuning parameters of twist angle, layer stacking and pressure, and
resulting in correlated insulator and superconducting states. Here we report
the experimental observation of similar correlated phenomena in twisted bilayer
tungsten diselenide (tWSe2), a semiconducting transition metal dichalcogenide
(TMD). Unlike twisted bilayer graphene where the flat band appears only within
a narrow range around a "magic angle", we observe correlated states over a
continuum of angles, spanning 4 degree to 5.1 degree. A Mott-like insulator
appears at half band filling that can be sensitively tuned with displacement
field. Hall measurements supported by ab initio calculations suggest that the
strength of the insulator is driven by the density of states at half filling,
consistent with a 2D Hubbard model in a regime of moderate interactions. At 5.1
degree twist, we observe evidence of superconductivity upon doping away from
half filling, reaching zero resistivity around 3 K. Our results establish
twisted bilayer TMDs as a model system to study interaction-driven phenomena in
flat bands with dynamically tunable interactions.
