Fluctuations and $T_c$ reduction in cuprate superconductors

TL;DR

This paper investigates fluctuations around the critical temperature in cuprate superconductors, revealing that the mean-field transition temperature is significantly higher than the observed $T_c$, and that fluctuations are linked to the superconducting gap rather than the pseudogap.

Contribution

It demonstrates that phase and amplitude fluctuations occur simultaneously and that the mean-field transition temperature scales with the gap, independent of the pseudogap temperature.

Findings

Mean-field transition temperature $T_c^{mf}$ exceeds $T_c$, especially at low doping.

Phase and amplitude fluctuations set in simultaneously.

$T_c^{mf}$ scales with the superconducting gap $ riangle_0$.

Abstract

We analyse fluctuations about $T_c$ in the specific heat of (Y,Ca)Ba$_2$Cu$_3$O$_{7-\delta}$, YBa$_2$Cu$_4$O$_8$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The mean-field transition temperature, $T_c^{mf}$, in the absence of fluctuations lies well above $T_c$ especially at low doping where it reaches as high as 150K. We show that phase and amplitude fluctuations set in simultaneously and $T_c^{mf}$ scales with the gap, $\Delta_0$, such that $2\Delta_0/k_BT_c^{mf}$ is comparable to the BCS weak-coupling value, 4.3, for d-wave superconductivity. We also show that $T_c^{mf}$ is unrelated to the pseudogap temperature, $T^*$.