Vortex States of a Dirty Quantum Hall Bilayer*

We study the ground state of a quantum Hall bilayer at filling $\nu$=1/2+1/2 in the presence of strong but smooth disorder. We argue that there is a characteristic disorder strength below which vortices will be rare and above which they proliferate. In the strong-disorder regime the system can be understood as an emulsion of vortex-antivortex crystals. We will discuss the implications for the observation of counterflow superfluidity and critical currents in these systems. These include a dramatic suppression of tunneling and a new disorder-induced lengthscale in the emulsion due to phase disorder.