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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 samplescite{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.
The spectral energy gap is an important signature that defines states of quantum matter: insulators, density waves, and superconductors have very different gap structures. The momentum resolved nature of angle-resolved photoemission spectroscopy (ARP
The notion of a finite pairing interaction energy range suggested by Nam, results in some states at the Fermi level not participating in pairings when there are scattering centers such as impurities. The fact that not all states at the Fermi level pa
We theoretically investigate the vortex state of the cuprate high-temperature superconductors in the presence of magnetic fields. Assuming the recently derived nonlinear $sigma$-model for fluctuations in the pseudogap phase, we find that the vortex c
We address the origin of the Cooper pairs in high-$T_c$ cuprates and the unique nature of the superconducting (SC) condensate. Itinerant holes in an antiferromagnetic background form pairs spontaneously, without any `glue, defining a new quantum obje
The observation of an unusual spin resonant excitation in the superconducting state of various High-Tc ~copper oxides by inelastic neutron scattering measurements is reviewed. This magnetic mode % (that does not exist in conventional superconductors)