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)Ba2Cu3O7−δ , YBa2Cu4O8, and Bi2Sr2CaCu2O8+δ . The mean-field transition temperature, T mf c , in the absence of fluctuations lies well above Tc and at low doping reaches as high as 150 K. T mf c is found to be unrelated to the pseudogap temperature T ∗, but scales with the gap 0, such that 2 0/kBT mf c is comparable to the BCS weak-coupling value 4.3, for d-wave superconductivity.