Fig. 1
From: Emergence of superconductivity in the cuprates via a universal percolation process
Temperature dependence of in-plane linear and nonlinear response in the cuprates. a Nonlinear conductivity σ3n (σ3 normalized to its peak value, which corresponds to the bulk Tc indicated by arrows) for three representative samples close to optimal hole doping: Hg1201, YBCO–Zn, and LSCO-0.15 (x = 0.15). b Nonlinear conductivity vs. Ginzburg–Landau reduced temperature ln(T/Tc), which demonstrates that Tc is not the common scale for superconductivity emergence. Dotted line is the GL prediction (see Methods). c σ3n shifted by a sample-dependent temperature Tπ collapses to a single curve. This demonstrates the existence of a universal emergence temperature/energy scale. Tc is indicated by arrows (LSCO-0.15, LSCO-0.19, and LSCO-0.08 have indistinguishable Tc values on this scale; Tc for LSCO-0.125 is at T − Tπ = −4.5 K). Orange line is the prediction of the simple site-percolation model discussed in the text. Inset: linear conductivity of Hg1201 and LSCO-0.15 along with the model prediction. d Phase diagram of LSCO with the characteristic temperatures below which the superconducting response is first resolved in both linear (microwave—MW) and nonlinear conductivity; errors are determined from the root-mean square noise level and are within the symbol size. These temperatures are significantly different despite the similar signal-to-noise ratio of ~103 (at Tc), consistent with the percolation model. The positions of the peaks in σ3n and in the real part of σ1 give consistent Tc values. Error bars for Tc are given by the error of the peak temperature determination (and are within the symbol size for σ3n). Lines are guides to the eye. The inset demonstrates, for LSCO-0.15, that σ3n α σ1n3 until the third-order response is indistinguishable from noise. The two temperatures below which signals are resolved from noise are marked with arrows
