Coherence network in the quantum hall bilayer

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a coherence network induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.