  Moir\'e superlattices formed in two-dimensional semiconductor heterobilayers
provide a new realization of Hubbard model physics in which the number of
electrons per effective atom can be tuned at will. We report on an exact
diagonalization study of the electronic properties of half-filled narrow
moir\'e bands in which correlation strengths are varied by changing twist
angles or interaction strengths. We construct a phase diagram for the bilayer,
identifying where the metal-insulator phase transition occurs, estimating the
sizes of the charge gaps in the insulating phase, and commenting on the nature
of the transition and the importance of sub-dominant interaction parameters.
