What is the energy scale in determining the T-c 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 cr itical temperature T-c is. According to the BCS mean-field theory, the ener gy gap at T much less than T-c, 2 Delta (o), is proportional to T-c; 2 Delt a (o) = 4.3k(B)T(c) for d-wave superconductors. In the case of high-T-c cup rates, however, 2 Delta (o) increases monotonically with the lowering of th e hole-doping level p even in the underdoped region, where T-c is largely s uppressed, and does not scale with T-c, except in a highly overdoped region . Interestingly, in a wide p range spreading over the under- and overdoped regions, 2 Delta (o) is almost proportional to crossover temperature T*, ar ound which a spin gap and/or a (small) pseudogap of almost the same energy scale as 2 Delta (o) start to develop progressively; 2 Delta (o)/k(B)T* is nearly independent of p and comparable to the BCS value in the entire p ran ge examined. On the other hand, 2 Delta (o)/k(B)T(c) is inversely proportio nal to p, 2 Delta (o)/k(B)T(c) similar to 1/p, except in the highly overdop ed region, where T-c is very close to the BCS expectation. This indicates t hat the energy scale in determining T-c is of order p Delta (o) in high-T-c cuprates. In this article, we will discuss some scenarios for the transiti on from pseudogap to superconducting states, where the energy scale in dete rmining T-c is expected to be of order p Delta (o).