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In the interlayer theory of high-temperature superconductivity, the interlayer pair tunneling energy (similar to the Josephson or Lawrence-Doniach energy) is the motivation for superconductivity. This connection requires two experimentally verifiable identities: the coherent normal-state conductance must be smaller than the "Josephson" coupling energy, and the Josephson coupling energy must be equal to the condensation energy of the superconductor. The first condition is well satisfied in the only case that is relevant, (La, Sr)2CuO4, but the second condition has been questioned. It is satisfied for all dopings in (La,Sr)2CuO4 and also in optimally doped Hg(Ba)2CuO5, which was measured recently, but seems to be strongly violated in measurements on single crystals of Tl2Ba2CuO6.
Philip W. Anderson (Fri,) studied this question.