  Rare-earth nickelates exhibit a remarkable metal-insulator transition
accompanied by a structural transition associated with a lattice `breathing'
mode. Using model considerations and first-principles calculations, we present
a theory of this phase transition, which reveals the key role of the coupling
between the electronic and lattice instabilities. We show that the transition
is driven by the proximity to an electronic disproportionation instability
which couples to the breathing mode, thus cooperatively driving the system into
the insulating state. This allows us to identify two key control parameters of
the transition: the susceptibility to electronic disproportionation and the
stiffness of the lattice mode. We show that our findings can be rationalized in
terms of a Landau theory involving two coupled order parameters, with general
implications for transition-metal oxides.
