Fluctuations and critical temperature reduction in cuprate superconductors

We show theoretically that phase and amplitude fluctuations set in simultaneously in the cuprates. We then analyze fluctuations about Tc in the specific heat of (Y,Ca)Ba₂Cu₃O_7-δ, YBa₂Cu₄O₈, and Bi₂Sr₂CaCu₂O_8+δ. The mean-field transition temperature, Tcᵐᶠ, in the absence of fluctuations lies well above Tc and at low doping reaches as high as 150 K. Tcᵐᶠ is found to be unrelated to the pseudogap temperature T*, but scales with the gap Δ₀, such that 2Δ₀/kBTcᵐᶠ is comparable to the BCS weak-coupling value 4.3, for d-wave superconductivity.