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What is the energy scale in determining the Tc of cuprate superconductivity?

For the understanding of the mechanism of a superconducting transition, it is of great interest to clarify what the energy scale in determining the critical temperature Tc is. According to the BCS mean-field theory, the energy gap at T<<Tc, 2Δo, is proportional to Tc; 2Δo = 4.3kBTc for d-wave superconductors. In the case of high-Tc cuprates, however, 2Δo increases monotonically with the lowering of the hole-doping level p even in the underdoped region, where Tc is largely suppressed, and does not scale with Tc, except in a highly overdoped region. Interestingly, in a wide p range spreading over the under- and overdoped regions, 2Δo is almost proportional to crossover temperature T*, around which a spin gap and/or a (small) pseudogap of almost the same energy scale as 2Δo start to develop progressively; 2Δo/kBT* is nearly independent of p and comparable to the BCS value in the entire p range examined. On the other hand, 2Δo/kBTc is inversely proportional to p, 2Δo/kBTc~1/p, except in the highly overdoped region, where Tc is very close to the BCS expectation. This indicates that the energy scale in determining Tc is of order pΔo in high-Tc cuprates. In this article, we will discuss some scenarios for the transition from pseudogap to superconducting states, where the energy scale in determining Tc is expected to be of order pΔo.