  The $\nu=2$ quantum Hall state at low Zeeman coupling is well-known to be a
translationally invariant singlet if Landau level mixing is small. At zero
Zeeman interaction, as Landau level mixing increases, the translationally
invariant state becomes unstable to aninhomogeneous state. This is the first
realistic example of a full Hall crystal, which shows the coexistence of
quantum Hall order and density wave order. The full Hall crystal differs from
the more familiar Wigner crystal by a topological property, which results in it
having only linearly dispersing collective modes at small $q$, and no $q^{3/2}$
magnetophonon. I present calculations of the topological number and the
collective modes.
