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Recent experiments on quantum Hall bilayers near total filling factor 1 havedemonstrated that they support an ``imperfect'' two-dimensional superfluidity,in which there is nearly dissipationless transport at non-vanishing temperatureobserved both in counterflow resistance and interlayer tunneling. We argue thatthis behavior may be understood in terms of a {\it coherence network} inducedin the bilayer by disorder, in which an incompressible, coherent state existsin narrow regions separating puddles of dense vortex-antivortex pairs. Arenormalization group analysis shows that it is appropriate to describe thesystem as a vortex liquid. We demonstrate that the dynamics of the nodes of thenetwork leads to a power law temperature dependence of the tunnelingresistance, whereas thermally activated hops of vortices across the linkscontrol the counterflow resistance.Comment: Published versio

Coherence Network in the Quantum Hall Bilayer