Fig. 4
From: Emergence of superconductivity in the cuprates via a universal percolation process
Universal percolation physics in the cuprates. a–d Four different experimental probes show qualitatively similar non-GL behavior (full lines) above Tc: a nonlinear conductivity of optimally doped LSCO (this work); b superconducting contribution to DC conductivity of YBCO, adapted from ref. 7; c Seebeck coefficient of europium co-doped LSCO (x = 0.11) adapted from ref. 8—the dotted line is the 2D GL prediction valid within 2 K of Tc; d torque magnetometry in underdoped Hg1201 (Tc = 67 K)—the dashed line indicates the noise floor. Adapted with permission from Yu et al.15. The decay constants of different observables are proportional to the universal scale Ξ0, but with different prefactors that can be directly calculated from the suggested model (see Methods). e Specific heat coefficient. The orange circles are measured values of the superconducting contribution to the specific heat coefficient, Δγ, for Y0.8Ca0.2Ba2Cu3O6.75 (from ref. 29), and the dashed line is a calculation that convolutes a mean-field step in γ at the local Tc with a Gaussian distribution of Tc. The line is obtained with a distribution width of 35 K, similar to the value of Ξ0; it is similar to the dashed line in Fig. 2a, since in a mean-field picture the specific heat essentially measures the superconducting fraction above Tc. The measurements also show a fluctuation peak around Tc, which is not included in the calculation. f Measured tomographic density of states for optimally doped Bi2Sr2CaCu2O8+x reproduced from ref. 19, with permission from APS. g Calculated density of states, assuming a Gaussian gap distribution with full width of 3.2 meV (see Methods). In a–d the lines are not the result of a direct calculation, but rather highlight pure exponential decay
