We report measurements of the ab-plane superfluid density ns (magnetic penetration depth, λ) of severely underdoped films of YBa2Cu3O6+x, with TCs from 6 to 50 K. TC is not proportional to ns(0); instead, we find TC ∝ n 1/2.3±0.4 s . At the lowest dopings, TC is as much as 5 times larger than the upper limit set by the KTB transition temperature of individual CuO2 bilayers.
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