  Three-dimensional topological insulators have protected Dirac-cone surface
states. In this paper we propose magnetic field induced topological insulator
thin film ordered states in which coherence is established spontaneously
between top and bottom surfaces. We find that the large dielectric constants of
these materials increases the layer separation range over which coherence
survives and decreases the superfluid sound velocity, but has little influence
on superfluid density or charge gap. The coherent state at total Landau-level
filling factor $\nu_T=0$ is predicted to be free of edge modes, qualitatively
altering its transport phenomenology.
