Energy gaps in high-$T_c$ superconductors: BCS after all?

TL;DR

This paper re-examines spectroscopic data on high-$T_c$ superconductors and finds that the superconducting gap scales with $T_c$ in a manner consistent with BCS theory, resolving previous discrepancies and supporting a two-gap scenario.

Contribution

It demonstrates that the superconducting gap in high-$T_c$ superconductors follows the BCS ratio across the phase diagram when accounting for pseudogap effects, unifying spectroscopic observations.

Findings

Superconducting gap scales with $T_c$ as per BCS theory.

Pseudogap effects cause spectral-weight loss, explaining previous disagreements.

Two-gap scenario reconciles various spectroscopic data.

Abstract

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 surface\cite{Kanigel} on which the superconducting gap forms at $T_c$. One thing that seems agreed is that the ratio $2\Delta_0/k_BT_c$ well exceeds the BCS value and grows with underdoping\cite{Miyakawa1,Miyakawa2}, suggesting unconventional, non-BCS superconductivity. Here we re-examine data from many spectroscopies, especially Raman $B_{1g}$ and $B_{2g}$ scattering\cite{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.