  The bilayer quantum Hall system at a total filling of $\nu_T=1$ has long
resisted explanation in terms of a true counterflow superfluid, though many
experimental features can be seen to be "almost" that of a superfluid. It is
widely believed that quenched disorder is the root cause of this puzzle. Here
we model the nonperturbative effects of disorder by investigating the $\nu=1$
bilayer in a strong periodic potential. Our model assumes that fermions are
gapped and real spins are fully polarized, and concentrates on the pseudospin
variable (the layer index), with the external potential coupling to the
topological (Pontryagin) density of the pseudospin. We find that as the
potential strength increases, there are ground state transitions in which the
topological content of the pseudospin configuration changes. These transitions
are generically weakly first-order, with a new quadratically dispersing mode
(in addition to the linearly dispersing Goldstone mode) sometimes becoming
nearly gapless near the transition. We show that this leads to strong
suppressions of both the Kosterlitz-Thouless transition temperature and the
interlayer tunneling strength, which we treat perturbatively. We discuss how
these results might extend to the case of true disorder.
