We express the superconducting gap, $Delta(T)$, in terms of thermodynamic functions in both $s$- and d-wave symmetries. Applying to Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ and Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-delta}$ we find that for all dopings $Delta
(T)$ persists, as a partial gap, high above $T_c$ due to strong superconducting fluctuations. Therefore in general two gaps are present above $T_c$, the superconducting gap and the pseudogap, effectively reconciling two highly polarized views concerning pseudogap physics.
Evidence from NMR of a two-component spin system in cuprate high-$T_c$ superconductors is shown to be paralleled by similar evidence from the electronic entropy so that a two-component quasiparticle fluid is implicated. We propose that this two-compo
nent scenario is restricted to the optimal and underdoped regimes and arises from the upper and lower branches of the reconstructed energy-momentum dispersion proposed by Yang, Rice and Zhang (YRZ) to describe the pseudogap. We calculate the spin susceptibility within the YRZ formalism and show that the doping and temperature dependence reproduces the experimental data for the cuprates.
A quarter of a century after their discovery the mechanism that pairs carriers in the cuprate high-Tc superconductors (HTS) still remains uncertain. Despite this the general consensus is that it is probably magnetic in origin [1] so that the energy s
cale for the pairing boson is governed by J, the antiferromagnetic exchange interaction. Recent studies using resonant inelastic X-ray scattering strongly support these ideas [2]. Here as a further test we vary J (as measured by two-magnon Raman scattering) by more than 60% by changing ion sizes in the model HTS system LnA2Cu3O7-{delta} where A=(Ba,Sr) and Ln=(La, Nd, Sm, Eu, Gd, Dy, Yb, Lu). Such changes are often referred to as internal pressure. Surprisingly, we find Tcmax anticorrelates with J where internal pressure is the implicit variable. This is the opposite to the effect of external pressure and suggests that J is not the dominant energy scale governing Tcmax.
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 $2Delta_0/k_BT_c^{mf}$ 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, $T^*$.
A major impediment to solving the problem of high-$T_c$ superconductivity is the ongoing confusion about the magnitude, structure and doping dependence of the superconducting gap, $Delta_0$, and of the mysterious pseudogap found in underdoped samples
cite{TallonLoram}. The pseudogap opens around the ($pi$,0) antinodes below a temperature $T^*$ leaving Fermi arcs across the remnant Fermi surfacecite{Kanigel} on which the superconducting gap forms at $T_c$. One thing that seems agreed is that the ratio $2Delta_0/k_BT_c$ well exceeds the BCS value and grows with underdopingcite{Miyakawa1,Miyakawa2}, suggesting unconventional, non-BCS superconductivity. Here we re-examine data from many spectroscopies, especially Raman $B_{1g}$ and $B_{2g}$ scatteringcite{Sacuto,Guyard}, and reconcile them all within a two-gap scenario showing that the points of disagreement are an artefact of spectral-weight loss arising from the pseudogap. Crucially, we find that $Delta_0(p)$, or more generally the order parameter, now scales with the mean-field $T_c$ value, adopting the weak-coupling BCS ratio across the entire phase diagram.
