Critical supercurrents and self-organization in quantum Hall bilayers

We present a theory of interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. In agreement with recent experiments [Phys. Rev. B 80, 165120 (2009); Phys. Rev. B 78, 075302 (2008)], we find that the critical current is proportional to the sample area and is comparable in magnitude to observed values. This reflects the formation of a Bean critical state as a result of current injection at the boundary. We predict a crossover to a critical current proportional to the square-root of the area in smaller samples. We also predict a peak in the critical current as the electron density varies at fixed layer separation.