  There are two classes of Mott insulators in nature, distinguished by their
responses to weak doping. With increasing chemical potential, Type I Mott
insulators undergo a first order phase transition from the undoped to the doped
phase. In the presence of long-range Coulomb interactions, this leads to an
inhomogeneous state exhibiting ``micro-phase separation.'' In contrast, in Type
II Mott insulators charges go in continuously above a critical chemical
potential. We show that if the insulating state has a broken symmetry, this
increases the likelihood that it will be Type I. There exists a close analogy
between these two types of Mott insulators and the familiar Type I and Type II
superconductors.
