Paired States in the Even Integer Quantum Hall Effect

We argue that a new type of quantum Hall state requiring non-perturbative Landau level mixing arises at low electron density. In these states, up and down spin electrons pair to form spinless bosons that condense into a bosonic quantum Hall state. We describe a wavefunction for a paired quantum Hall state at $\nu=2$ and argue that it is stabilized by a BCS instability arising in flux attachment calculations. Based on this state, we derive a new global phase diagram for the integral quantum Hall effect with spin. Additional experimental implications are discussed.